\input texinfo   @c -*-texinfo-*-
@c %**start of header
@setfilename units.info
@settitle Units: A Unit Conversion Program and Scientific Calculator
@finalout
@setchapternewpage off
@firstparagraphindent none
@set EDITION 2.25
@set VERSION 2.25
@c %**end of header

@c for AUTHOR section
@c man program units

@c ifman .\" 
@copying
This manual is for GNU Units (version @value{VERSION}),
which performs units conversions and units calculations.

Copyright @copyright{} 1996, 1997, 1999, 2000, 2001, 2002, 2004, 2005, 2007,
2011--2024, 2026 Free Software Foundation, Inc.

@quotation
Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.3 or
any later version published by the Free Software Foundation; with no
Invariant Sections, with no Front-Cover Texts, and with no Back-Cover
Texts.
@c end ifman
@c noman
A copy of the license is included in the section entitled
``GNU Free Documentation License''.
@end quotation
@end copying
@c end noman

@defcodeindex op
@syncodeindex op cp

@c noman
@dircategory Science
@direntry
* Units: (units).               Units conversion and scientific calculation.
@end direntry

@c end noman
@c man .TH UNITS 1   "14 January 2026"
@c man .\" ====================================================================
@c man .SH NAME
@c man .\" ====================================================================
@c man .PP
@c man units \(em unit conversion and calculation program
@c man .\" hack to prevent very thick fraction bars with gropdf
@c man .\" '-1' makes thickness proportional to type size
@c man .if \n(.g .if t \Z@\D't -1'@
@titlepage
@title Units Conversion
@subtitle Edition @value{EDITION} for @command{units} Version @value{VERSION}
@author Adrian Mariano
@page
@vskip 0pt plus 1filll
@insertcopying
@end titlepage
@contents

@iftex
@headings off
@everyheading Units Conversion @| @| @thispage
@end iftex

@ifnottex
@node Top
@top Units Conversion

@c noman
This manual describes the @command{units} command for units conversion
and how you can use it as a powerful scientific calculator that keeps
track of units.  This is Edition @value{EDITION} of @cite{The Units
Conversion Manual} for @command{units} Version @value{VERSION}.
@c end noman
@end ifnottex

@menu
* Overview::            What does @command{units} do?
* Interactive Use::     How to use @command{units}.
* Command Line Use::    How to use @command{units} non-interactively.
* Unit Definitions::    What units are defined?
* Unit Expressions::    Forming compound units.
* Nonlinear Conversions:: Nonlinear unit conversions (e.g., temperature).
* Unit Lists::          Conversion to sums of units (e.g., feet and inches).
* Alternative Unit Systems::     CGS units and natural units
* Logging Calculations:: Logging conversions and calculations in a file.
* Invoking Units::      Command line options.
* Setting Options Interactively::     Setting options interactively
* Scripting with Units:: Using units in scripts
* Output Styles::       Different ways units can print the output.
* Defining Your Own Units::  Adding your own unit definitions
* Numeric Output Format:: How to change the output format
* Localization::        How to define and use regional unit names.
* Environment Vars::    Environment variables used by @command{units}.
* Data Files::          Descriptions and locations of units data files.
* Unicode Support::     Support for Unicode (UTF-8).
* Readline Support::    Unit name completion and editing.
* Currency::            Updating currency exchange rates and CPI.
* Database Syntax::     Summary of database command syntax.
* GNU Free Documentation License::  License.
* Index::               General index.
@end menu

@c noman
@node Overview
@c =====================================================================
@chapter Overview of @command{units}
@c =====================================================================
@c end noman
@c ifman
@ignore
.\" ====================================================================
.SH SYNOPSIS
.\" ====================================================================
.SY units
.RI \:[ from-unit
.RI \:[ to-unit ]]
.YS
.SY units
.OP \-hcemnSpqsv1trUVI
.OP \-d digits
.OP \-f "units\ file"
.OP \-L logfile
.OP \-l locale
.OP \-o format
.OP \-u "unit\ system"
.br
.RI \:[ from-unit
.RI \:[ to-unit ]]
.YS
.SY units
.OP \-\^\-help
.OP \-\^\-check
.OP \-\^\-check-verbose
.OP \-\^\-verbose-check
.OP \-\^\-list-units
.OP \-\^\-digits digits
.OP \-\^\-exponential
.OP \-\^\-file "units\ file"
.OP \-\^\-log logfile
.OP \-\^\-locale locale
.OP \-\^\-minus
.OP \-\^\-oldstar
.OP \-\^\-newstar
.OP \-\^\-nolists
.OP \-\^\-show-factor
.OP \-\^\-conformable
.OP \-\^\-output-format format
.OP \-\^\-product
.OP \-\^\-quiet
.OP \-\^\-silent
.OP \-\^\-strict
.OP \-\^\-verbose
.OP \-\^\-compact
.OP \-\^\-one-line
.OP \-\-terse
.OP \-\^\-round
.OP \-\^\-unitsfile
.OP \-\^\-units "units\ system"
.OP \-\^\-version
.OP \-\^\-info
.br
.RI \:[ from-unit
.RI \:[ to-unit ]]
.YS
.\" ====================================================================
.SH DESCRIPTION
.\" ====================================================================
@end ignore
@c end ifman

The @command{units} program converts quantities expressed in various
systems of measurement to their equivalents in other systems of
measurement.
Like many similar programs, it can handle multiplicative scale changes.
It can also handle nonlinear conversions such as Fahrenheit to
@c man Celsius;
@c noman
Celsius;@footnote{But Fahrenheit to
Celsius is linear, you insist.  Not so.  A transformation @math{T} is linear if
@math{T(x+y)=T(x)+T(y)} and this fails for @math{T(x)=ax+b}.  This transformation is
affine, but not linear---see @url{https://en.wikipedia.org/wiki/Linear_map}. }
@pxref{Temperature Conversions}.
@c end noman
@c man see \fITemperature Conversions\fP.
The program can also perform conversions from and to sums of
units, such as converting between meters and feet plus inches.

@c ifman
@ignore
.if n .ig ++
.EQ
delim $$
.EN
.++
But Fahrenheit to
Celsius is linear, you insist.  Not so.  A transformation \fIT\fP is linear if
.if t $T(x + y) = T(x) + T(y)$
.if n \fIT\fP(\fIx\fP\ +\ \fIy\fP)\ =\ \fPT\fP(\fPx\fP)\ +\ \fIT\fP(\fPy\fP)
and this fails for
.if t $T(x) = ax + b$.
.if n \fIT\fP(\fIx\fP)\ =\ \fIax\fP\ +\ \fIb\fP.
This transformation is affine, but not linear\(emsee \f(CWhttps://en.wikipedia.org/wiki/Linear_map\fP.
.if n .ig ++
.EQ
delim off
.EN
.++
.PP
@end ignore
@c end ifman

Basic operation is simple: you enter the units that you want to convert
@emph{from} and the units that you want to convert @emph{to}.
You can use the program interactively with prompts, or you can use it
from the command line.

Beyond simple unit conversions, @command{units} can be used as a
general-purpose scientific calculator that keeps track of units in its
calculations.  You can form arbitrary complex mathematical expressions
of dimensions including sums, products, quotients, powers, and even
roots of dimensions.  Thus you can ensure accuracy and dimensional
consistency when working with long expressions that involve many
different units that may combine in complex ways; for an illustration,
@c man see \fIComplicated Unit Expressions\fP.
@c noman
@pxref{Complicated Unit Expressions}.
@c end noman

The units are defined in several external data files.  You can use the
extensive data files that come with the program, or you can provide
your own data file to suit your needs.  You can also use your own data
file to supplement the standard data files.

You can change the default behavior of @command{units} with various
options given on the command line. @xref{Invoking Units}, for a
description of the available options.
@c
@ignore
@c ifman
.\" =====================================================================
.SH "ADDITIONAL DOCUMENTATION"
.\" =====================================================================
.PP
This manual is also available in PDF and HTML:
.PP
.RS 3n
.nf
.UR https://www.gnu.org/software/units/manual/units.pdf
.UE
.UR https://www.gnu.org/software/units/manual/units.html
.UE
.fi
.RE
@c end ifman
@end ignore
@c
@node Interactive Use
@c =====================================================================
@chapter Interacting with @command{units}
@c =====================================================================
@cindex interactive use

@menu
* Interactive Commands::           Interactive commands, including help
@end menu

To invoke @command{units} for interactive use, type @kbd{units} at your
shell prompt.  The program will print something like this:

@example
@group
Currency exchange rates from FloatRates (USD base) on 2023-07-08
3612 units, 109 prefixes, 122 nonlinear units

You have:
@end group
@end example

@noindent
At the @w{@samp{You have:}} prompt, type the quantity and units that you
are converting @emph{from}.  For example, if you want to convert ten
meters to feet, type @kbd{10 meters}.  Next, @command{units} will print
@w{@samp{You want:}}.  You should type the units you want to convert
@emph{to}.  To convert to feet, you would type @kbd{feet}.  If the
@command{readline} library was compiled in, then @key{tab} will complete
unit names. @xref{Readline Support}, for more information about
@command{readline}.  To quit the program type @kbd{quit} or @kbd{exit}
at either prompt.

The result will be displayed in two ways.  The first line of output,
which is marked with a @samp{*} to indicate multiplication, gives the
result of the conversion you have asked for.  The second line of output,
which is marked with a @samp{/} to indicate division, gives the inverse
of the conversion factor.  If you convert 10 meters to feet,
@command{units} will print

@example
@group
    * 32.808399
    / 0.03048
@end group
@end example

@noindent
which tells you that 10 meters equals about 32.8 feet.
The second number gives the conversion in the opposite direction.
In this case, it tells you that 1 foot is equal to about
0.03 dekameters since the dekameter is 10 meters.
It also tells you that 1/32.8 is about 0.03.

The @command{units} program prints the inverse because sometimes it is a
more convenient number.  In the example above, for example, the inverse
value is an exact conversion: a foot is exactly 0.03048 dekameters.
But the number given the other direction is inexact.

If you convert grains to pounds, you will see the following:

@example
@group
You have: grains
You want: pounds
        * 0.00014285714
        / 7000
@end group
@end example

@noindent
@w{From} the second line of the output, you can immediately see that a grain
is equal to a seven thousandth of a pound.  This is not so obvious from
the first line of the output.  If you find the output format confusing,
try using the @option{--verbose} option:
@cindex verbose output

@example
@group
You have: grain
You want: aeginamina
        grain = 0.00010416667 aeginamina
        grain = (1 / 9600) aeginamina
@end group
@end example

@noindent
If you request a conversion between units that measure reciprocal
dimensions, then @command{units} will display the conversion results with an extra
note indicating that reciprocal conversion has been done:
@cindex reciprocal conversion

@example
@group
You have: 6 ohms
You want: siemens
        reciprocal conversion
        * 0.16666667
        / 6
@end group
@end example

@noindent
Reciprocal conversion can be suppressed by using the @option{--strict} option.
As usual, use
the @option{--verbose} option to get more comprehensible output:
@cindex verbose output
@cindex strict conversion

@example
@group
You have: tex
You want: typp
        reciprocal conversion
        1 / tex = 496.05465 typp
        1 / tex = (1 / 0.0020159069) typp

You have: 20 mph
You want: sec/mile
        reciprocal conversion
        1 / 20 mph = 180 sec/mile
        1 / 20 mph = (1 / 0.0055555556) sec/mile
@end group
@end example

@noindent
If you enter incompatible unit types, the @command{units} program will
print a message indicating that the units are not conformable and
it will display the reduced form for each unit:
@cindex incompatible units
@cindex non-conformable units

@example
@group
You have: ergs/hour
You want: fathoms kg^2 / day
conformability error
        2.7777778e-11 kg m^2 / sec^3
        2.1166667e-05 kg^2 m / sec
@end group
@end example

@noindent
If you only want to find the reduced form or definition of a unit,
simply press @key{Enter} at the @w{@samp{You want:}} prompt.  Here is an
example:

@example
@group
You have: jansky
You want:
        Definition: fluxunit = 1e-26 W/m^2 Hz = 1e-26 kg / s^2
@end group
@end example

@noindent
The output from @command{units} indicates that the jansky is defined to
be equal to a fluxunit which in turn is defined to be a certain
combination of watts, meters, and hertz.  The fully reduced (and in this
case somewhat more cryptic) form appears on the far right.  If the
ultimate definition and the fully reduced form are identical, the latter
is not shown:

@example
@group
You have: B
You want:
        Definition: byte = 8 bit
@end group
@end example

@noindent
The fully reduced form @emph{is} shown if it and the ultimate definition
are equivalent but not identical:

@example
@group
You have: N
You want:
        Definition: newton = kg m / s^2 = 1 kg m / s^2
@end group
@end example

@noindent
Some named units are treated as dimensionless in some situations.
These units include the radian and steradian.  These units will be
treated as equal to 1 in units conversions.  Power is equal to torque
times angular velocity.  This conversion can only be performed if the
radian is dimensionless.

@example
@group
You have: (14 ft lbf) (12 radians/sec)
You want: watts
        * 227.77742
        / 0.0043902509
@end group
@end example

@noindent
It is also possible to compute roots and other non-integer powers of
dimensionless units; this allows computations such as the altitude of
geosynchronous orbit:

@example
@group
You have: cuberoot(G earthmass / (circle/siderealday)^2) - earthradius
You want: miles
        * 22243.267
        / 4.4957425e-05
@end group
@end example

@noindent
Named dimensionless units are not treated as dimensionless
in other contexts.  They cannot be used as exponents
so for example, @samp{meter^radian} is forbidden.
@cindex dimensionless units

@cindex @samp{?} to show conformable units
@cindex conformable units, @samp{?} to show
If you want a list of options you can type @kbd{?} at the
@w{@samp{You want:}} prompt.  The program will display a list of named
units that are conformable with the unit that you entered at the
@w{@samp{You have:}} prompt above.  Conformable unit @emph{combinations}
will not appear on this list.

@node Interactive Commands
@c ---------------------------------------------------------------------
@section Interactive Commands
@c ---------------------------------------------------------------------
@cindex interactive commands
@cindex commands, interactive 

@cindex help
Typing @kbd{help} at either prompt displays a short help message.  You
can also type @kbd{help} followed by a unit name.  This will invoke a
pager on the units database at the point where that unit is defined.
You can read the definition and comments that may give more details or
historical information about the unit.  If your pager allows, you may
want to scroll backwards, e.g. with @samp{b}, because sometimes a longer
comment about a unit or group of units will appear before the
definition.  You can generally quit out of the pager by pressing
@samp{q}.

@cindex search
Typing @w{@kbd{search} @var{text}} will display a list of all
units whose names contain @var{text} as a substring along with their
definitions.  This may help in the case where you aren't sure of the
right unit name. 
Typing @w{@kbd{search .}} will display a list of all units; this can be
helpful if you aren't sure of an appropriate substring, though examining
the output can be tedious.  Here @samp{.} is a special argument to the
@kbd{search} command, not a regular expression.  If you want to use a
regular expression to search units @emph{and} their definitions, the
@option{--list-units} option will display a list of all units, which can
be sent to a filter such as @command{grep}.
Typing @w{@kbd{search _}} will display a list of all assigned runtime
variables---whose names begin with @samp{_}---without including all
units whose names simply @emph{contain} @samp{_}.
@xref{Variables Assigned at Run Time} for more information on runtime
variables.

@cindex version
Typing @kbd{version} will display the @command{units} version
number; unlike the @option{--version} option, only the version
number is shown, regardless of any other settings.  Full
information is available with the @kbd{info} command.

@cindex info
Typing @kbd{info} will display the same information as the
@option{--info} option, described in @ref{Invoking Units}.

Many values set by command-line options can also be set
interactively by typing @w{@kbd{set} @var{option}@kbd{=}@var{value}};
typing @w{@kbd{set} @var{option}} will show the value for that option.  Typing
@kbd{set} will show a list of options that can be set; options
set to other than default values will have a prepended @samp{*}.
@xref{Setting Options Interactively} for more information.

@node Command Line Use
@c =====================================================================
@chapter Using @command{units} Non-Interactively
@c =====================================================================
@cindex command-line unit conversion
@cindex non-interactive unit conversion

The @command{units} program can perform units conversions non-interactively
from the command line.  To do this, type the command, type the original
unit expression, and type the new units you want.  If a units expression
contains non-alphanumeric characters, you may need to protect it from
interpretation by the shell using single or double quote characters.

If you type

@example
units "2 liters" quarts
@end example

@noindent
then @command{units} will print

@example
@group
    * 2.1133764
    / 0.47317647
@end group
@end example

@noindent
and then exit.
The output tells you that 2 liters is about 2.1 quarts, or alternatively that
a quart is about 0.47 times 2 liters.

@command{units} does not require a space between a numerical value and
the unit, so the previous example can be given as

@example
units 2liters quarts
@end example

@noindent
to avoid having to quote the first argument.

If the conversion is successful, @command{units} will return success (zero)
to the calling environment.  If you enter non-conformable units, then
@command{units} will print a message giving the reduced form of each
unit and it will return failure (nonzero) to the calling environment.

If the @option{--conformable} option is given, only one unit expression
is allowed, and @command{units} will print all units conformable with
that expression; it is equivalent to giving @kbd{?} at the
@w{@samp{You want:}} prompt.  For example,

@example
@group
units --conformable gauss
B_FIELD   tesla
Gs        gauss
T         tesla
gauss     abvolt sec / cm^2
stT       stattesla
statT     stattesla
stattesla statWb/cm^2
tesla     Wb/m^2
@end group
@end example

@noindent
If you give more than one unit expression with the
@option{--conformable} option, the program will exit with an error
message and return failure.  This option has no effect in interactive
mode.

If the @option{--terse} (@option{-t}) option is given with the
@option{--conformable} option, conformable units are shown without
definitions; with the previous example, this would give

@example
@group
units --terse --conformable gauss
B_FIELD
Gs
T
gauss
stT
statT
stattesla
tesla
@end group
@end example

@noindent
When the @option{--conformable} option is not given and you invoke
@command{units} with only one argument, @command{units} will print the
definition of the specified unit.  It will return failure if the unit is
not defined and success if the unit is defined.

@node Finding Units
@c ---------------------------------------------------------------------
@section Finding Units
@c ---------------------------------------------------------------------
@cindex finding units

The @command{units} database includes many units, and it can sometimes
be difficult to remember every name.
The interactive @kbd{search} command examines only unit names, so it
cannot be used to find units whose @emph{definitions} contain a pattern.
If @command{units} is invoked with the @option{--list-units} option, the
output can be sent to a filter such as @command{grep}, examining the
unit name @emph{and} the definition.  For example,

@example
@group
@c noman
units --list-units | grep ';'
@c end noman
@c ifman
@ignore
.ne 14
units -\&-list-units | grep \[aq];\[aq]
@end ignore
@c end ifman
dms                                    deg;arcmin;arcsec
ftin                                   ft;in;1|8 in
ftin16                                 ft;in;1|16 in
ftin32                                 ft;in;1|32 in
ftin4                                  ft;in;1|4 in
ftin64                                 ft;in;1|64 in
ftin8                                  ft;in;1|8 in
hms                                    hr;min;sec
inchfine                               in;1|8 in;1|16 in;1|32 in;1|64 in
time                                   year;day;hr;min;sec
uswt                                   lb;oz
  .  .  .
@end group
@end example

@noindent
could find all unit lists, which include at least one semicolon in their
definitions.

The @kbd{search} command
doesn't support regular expressions, but with the
@option{--list-units} option the output can be sent to a filter such as
@command{grep}, which does.  If you expect a long list of results, you
can send the output of the filter to a pager.  For example,

@example
@group
@c noman
units --list-units | grep 'paper[[:space:]]' | more
@c end noman
@c ifman
@ignore
.ne 15
units --list-units | grep \[aq]paper[[:space:]]\[aq] | more
@end ignore
@c end ifman
A0paper                                841 mm 1189 mm
A10paper                               26 mm 37 mm
A1paper                                594 mm 841 mm
A2paper                                420 mm 594 mm
A3paper                                297 mm 420 mm
A4paper                                210 mm 297 mm
A5paper                                148 mm 210 mm
A6paper                                105 mm 148 mm
A7paper                                74 mm 105 mm
A8paper                                52 mm 74 mm
A9paper                                37 mm 52 mm
  .  .  .
@end group
@end example

@noindent
could show a list of all defined paper sizes.

@node Unit Definitions
@c =====================================================================
@chapter Unit Definitions
@c =====================================================================
@cindex unit definitions

The conversion information is read from several units data files:
@file{definitions.units}, @file{elements.units}, @file{currency.units},
and @file{cpi.units},
which are usually located in
the @file{/usr/share/units} directory.
If you invoke @command{units} with the @option{-V} option, it will print
the location of these files.
The default main
file includes definitions for all familiar units, abbreviations and
metric prefixes.  It also includes many obscure or archaic units.
Many common spelled-out numbers (e.g., @samp{seventeen}) are recognized.

@c ---------------------------------------------------------------------
@section Physical Constants
@c ---------------------------------------------------------------------

Many constants of nature are defined, including these:

@example
pi          @r{ratio of circumference of a circle to its diameter}
c           @r{speed of light}
e           @r{charge on an electron}
force       @r{acceleration of gravity}
mole        @r{Avogadro's number}
water       @r{pressure per unit height of water}
Hg          @r{pressure per unit height of mercury}
au          @r{astronomical unit}
k           @r{Boltzman's constant}
mu0         @r{permeability of vacuum}
epsilon0    @r{permittivity of vacuum}
G           @r{Gravitational constant}
mach        @r{speed of sound}
@end example

@noindent
The standard data file includes numerous other constants.  Also included
are the densities of various ingredients used in baking so that
@samp{2@tie{}cups flour_sifted} can be converted to @samp{grams}.  This
is not an exhaustive list.  Consult the units data file to see the
complete list, or to see the definitions that are used.

@c ---------------------------------------------------------------------
@section Atomic Masses of the Elements
@c ---------------------------------------------------------------------

The data file @file{elements.units} includes atomic masses for most
elements and most known isotopes.  If the mole fractions of constituent
isotopes are known, an elemental mass is calculated from the sum of the
products of the mole fractions and the masses of the constituent
isotopes.  If the mole fractions are not known, the mass of the most
stable isotope---if known---is given as the elemental mass. 
For radioactive elements with atomic numbers 95 or greater, the mass
number of the most stable isotope is not specified, because the list of
studied isotopes is still incomplete.  If no stable isotope is known, no
elemental mass is given, and you will need to choose the most
appropriate isotope.

The data are obtained from the US National Institute for Standards and
Technology (NIST):
@uref{https://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=&all=all&ascii=ascii2&isotype=all}.
The @file{elements.units} file can be generated from these data using
the @command{elemcvt} command included with the distribution.

@c ---------------------------------------------------------------------
@section Currency Exchange Rates and Consumer Price Index
@c ---------------------------------------------------------------------

The data file @file{currency.units} includes currency conversion rates;
the file @file{cpi.units} includes the US Consumer Price Index (CPI),
published by the US Bureau of Labor Statistics.  The data are updated
monthly by the BLS;
@c man see \fIUpdating Currency Exchange Rates and CPI\fP
@c noman
@pxref{Currency, ,Updating Currency Exchange Rates and CPI}
@c end noman
for information on updating @file{currency.units} and @file{cpi.units}.


@c ---------------------------------------------------------------------
@section English Customary Units
@c ---------------------------------------------------------------------

@cindex volume measure, English customary
English customary units differ in various ways among different
regions.  In Britain a complex system of volume measurements featured
different gallons for different materials such as a wine gallon and
ale gallon that different by twenty percent.  This complexity was
swept away in 1824 by a reform that created an entirely new gallon,
the British Imperial gallon defined as the volume occupied by ten
pounds of water.  Meanwhile in the USA the gallon is derived from the
1707 Winchester wine gallon, which is 231 cubic inches.  These gallons
differ by about twenty percent.  By default if @command{units} runs in
the @samp{en_GB} locale you will get the British volume measures.  If
it runs in the @samp{en_US} locale you will get the US volume
measures.  In other locales the default values are the US
definitions.  If you wish to force different definitions, then set the
environment variable @env{UNITS_ENGLISH} to either @samp{US} or
@samp{GB} to set the desired definitions independent of the locale.

@cindex units, English customary
@cindex units, US customary
@cindex length measure, English customary
@cindex length measure, UK
@cindex survey measure, US
@cindex US survey measure
@cindex survey mile, US
@cindex US survey foot
@cindex State Plane Coordinate System, US
@cindex US State Plane Coordinate System
@cindex survey foot, US
@cindex US survey mile
@cindex mile, international
@cindex international mile
@cindex yard, international
@cindex international yard
Before 1959, the value of a yard (and other units of measure defined in
terms of it) differed slightly among English-speaking countries.  In
1959, Australia, Canada, New Zealand, the United Kingdom, the United
States, and South Africa adopted the Canadian value of 1@tie{}yard =
0.9144@tie{}m (exactly), which was approximately halfway between the
values used by the UK and the US; it had the additional advantage of
making 1@tie{}inch = 2.54@tie{}cm (exactly).  This new standard was
termed the @dfn{International Yard}.  Australia, Canada, and the UK then
defined all customary lengths in terms of the International Yard
(Australia did not define the furlong or rod); because many US land
surveys were in terms of the pre-1959 units, the US continued to define
customary surveyors' units (furlong, chain, rod, pole, perch, and link)
in terms of the previous value for the foot, which was termed the
@dfn{US survey foot}.  The US defined a @dfn{US survey mile} as 5280 US
survey feet, and defined a @dfn{statute mile} as a US survey mile.  The
US values for these units differed from the international values by about
2@tie{}ppm.

The 1959 redefinition of the foot was legally binding in the US but
allowed continued use of the previous definition of the foot for
geodetic surveying.  It was assumed that this use would be temporary,
but use persisted, leading to confusion and errors, and it was at
odds with the intent of uniform standards.  Since January 1, 2023, the
US survey foot has been officially deprecated
@c noman
(@url{https://www.govinfo.gov/app/details/FR-2020-10-05/2020-21902,,85 FR
62698}),
@c end noman
@c man (85 FR 62698),
with its use limited to historical and legacy applications.

The @command{units} program has always used the international values for these
units; the legacy US values can be obtained by using either the @samp{US} or
the @samp{survey} prefix.  In either case, the simple familiar
relationships among the units are maintained, e.g., 1 @samp{furlong} =
660 @samp{ft}, and 1 @samp{USfurlong} = 660 @samp{USft}, though the
metric equivalents differ slightly between the two cases.
The @samp{US} prefix or the @samp{survey} prefix can also be used to
obtain the US survey mile and the value of the US yard prior to 1959,
e.g., @samp{USmile} or @samp{surveymile} (but @emph{not}
@samp{USsurveymile}).  To get the US value of the statute mile, use
either @samp{USstatutemile} or @samp{USmile}.
The pre-1959 UK values for these units can be obtained with the prefix
@samp{UK}.

Except for distances that extend over hundreds of miles (such as in the
US State Plane Coordinate System), the differences in the miles are
usually insignificant:

@example
@group
You have: 100 surveymile - 100 mile
You want: inch
        * 12.672025
        / 0.078913984
@end group
@end example

The US acre was officially defined in terms of the US survey
foot, but @command{units} has used a definition based on the
international foot; the @command{units} definition is now the same as
the official US value.  If you want the previous US acre, use
@samp{USacre} and similarly use @samp{USacrefoot} for the previous US
version of that unit.  The difference between these units is about 4
parts per million.


@c ---------------------------------------------------------------------
@section Miscellaneous Notes on Unit Definitions
@c ---------------------------------------------------------------------

@cindex measure, Imperial
@cindex Imperial measure
@cindex British Imperial measure
The @samp{pound} is a unit of mass.  To get force, multiply by the
force conversion unit @samp{force} or use the shorthand @samp{lbf}.
(Note that @samp{g} is already taken as the standard abbreviation for
the gram.)  The unit @samp{ounce} is also a unit of mass.  The fluid
ounce is @samp{fluidounce} or @samp{floz}.  When British capacity
units differ from their US counterparts, such as the British Imperial
gallon, the unit is defined both ways with @samp{br} and @samp{us}
prefixes.  Your locale settings will determine the value of the
unprefixed unit.  Currency is prefixed with its country
name: @samp{belgiumfranc}, @samp{britainpound}.

@cindex units, lookup method

When searching for a unit, if the specified string does not appear
exactly as a unit name, then the @command{units} program will try to
remove a trailing @samp{s}, @samp{es}.  Next units will replace a
trailing @samp{ies} with @samp{y}.  If that fails,
@command{units} will check for a prefix.  The database includes all
of the standard metric prefixes.  Only one prefix is permitted per
unit, so @samp{micromicrofarad} will fail.  However, prefixes can
appear alone with no unit following them, so
@samp{micro*microfarad} will work, as will @samp{micro microfarad}.

@cindex prefixes

To find out which units and prefixes are available, read the default
units data files; the main data file is extensively annotated.

@node Unit Expressions
@c =====================================================================
@chapter Unit Expressions
@c =====================================================================
@cindex unit expressions

@menu
* Operators::           The usual arithmetic operators, with a few extras
* Sums and Differences of Units::  Adding and subtracting units
* Numbers as Units::    A number is a dimensionless unit
* Built-in Functions::    Trigonometric functions, logarithms, roots
* Previous Result::     Inserting the result of the previous conversion
* Complicated Unit Expressions::   A complicated example
* Variables Assigned at Run Time::      Saving intermediate results in variables
* Backwards Compatibility::   Alternate behavior for @samp{*} and @samp{-}
@end menu

@node Operators
@c ---------------------------------------------------------------------
@section Operators
@c ---------------------------------------------------------------------
@cindex operators

You can enter more complicated units by combining units with operations
such as multiplication, division, powers, addition, subtraction, and
parentheses for grouping.  You can use the customary symbols for these
operators when @command{units} is invoked with its default options.
Additionally, @command{units} supports some extensions, including high
priority multiplication using a space, and a high priority numerical
division operator (@samp{|}) that can simplify some expressions.

@cindex products of units
@cindex quotients of units
@cindex units quotients
@cindex multiplication of units
@cindex division of units
@cindex operator, @samp{per}
@cindex @samp{per} operator
@cindex operator, space
@cindex operator, star (@samp{*})
@cindex star (@samp{*}) operator
@cindex @samp{*} operator
@cindex operator, slash (@samp{/})
@cindex slash (@samp{/}) operator
@cindex operator, solidus (@samp{/})
@cindex solidus (@samp{/}) operator

You multiply units using a space or an asterisk (@samp{*}).
The next example shows both forms:

@example
@group
You have: arabicfoot * arabictradepound * force
You want: ft lbf
        * 0.7296
        / 1.370614
@end group
@end example

@noindent
You can divide units using the slash (@samp{/}) or with @samp{per}:

@example
@group
You have: furlongs per fortnight
You want: m/s
        * 0.00016630986
        / 6012.8727
@end group
@end example

@cindex parentheses
@noindent
You can use parentheses for grouping:

@example
@group
You have: (1/2) kg / (kg/meter)
You want: league
        * 0.00010356166
        / 9656.0833
@end group
@end example

@cindex operator precedence
@cindex parentheses
@cindex white space

@noindent
White space surrounding operators is optional, so the previous example
could have used @samp{(1/2)kg/(kg/meter)}.  As a consequence, however,
hyphenated spelled-out numbers (e.g., @samp{forty-two}) cannot be used;
@samp{forty-two} is interpreted as @samp{40 - 2}.

Multiplication using a space has a higher precedence
than division using a slash and is evaluated left to right;
in effect, the first @samp{/} character marks the beginning of the
denominator of a unit expression.
This makes it simple to enter a quotient with several terms in the
denominator: @w{@samp{J / mol K}}.
The @samp{*} and @samp{/} operators have the same precedence, and are
evaluated left to right; if you multiply with @samp{*}, you must group
the terms in the denominator with parentheses: @w{@samp{J / (mol * K)}}.

@cindex fractions, numerical
@cindex numerical fractions
@cindex division of numbers
@cindex operator, vertical bar (@samp{|})
@cindex vertical bar (@samp{|}) operator
@cindex @samp{|} operator

The higher precedence of the space operator may not always be advantageous.
For example, @w{@samp{m/s s/day}} is equivalent to
@w{@samp{m / s s day}} and has dimensions of length per time cubed.
Similarly, @w{@samp{1/2 meter}} refers to a unit of reciprocal length
equivalent to 0.5/meter, perhaps not what you would intend if
you entered that expression.  The get a half meter you would need to
use parentheses: @w{@samp{(1/2) meter}}.
The @samp{*} operator is convenient for multiplying a sequence of
quotients.  For example, @w{@samp{m/s * s/day}} is equivalent to
@samp{m/day}.  Similarly, you could write @w{@samp{1/2 * meter}} to get
half a meter.

The @command{units} program supports another option for numerical fractions:
you can indicate division of @emph{numbers} with the vertical bar
(@samp{|}), so if you wanted half a meter you could write
@w{@samp{1|2 meter}}.
You cannot use the vertical bar to indicate division of non-numerical
units (e.g., @samp{m|s} results in an error message).

@cindex powers
@cindex exponent operator
@cindex operator, caret (@samp{^})
@cindex operator, (@samp{**})
@cindex @samp{**} operator
@cindex parentheses

Powers of units can be specified using the @samp{^} character, as shown in
the following example, or by simple concatenation of a unit and its
exponent: @samp{cm3} is equivalent to @samp{cm^3};
if the exponent is more than one digit, the @samp{^} is required.
You can also use @samp{**} as an exponent operator.

@example
@group
You have: cm^3
You want: gallons
        * 0.00026417205
        / 3785.4118
@end group
@end example

@noindent
Concatenation only works with a single unit name: if you write @samp{(m/s)2},
@command{units} will treat it as multiplication by 2.
@cindex prefixes and exponents
When a unit includes a prefix, exponent operators apply to the
combination, so @samp{centimeter3} gives cubic centimeters.  If you
separate the prefix from the unit with any multiplication operator (e.g.,
@samp{centi meter^3}), the prefix is treated as a separate unit, so
the exponent applies only to the unit without the prefix.  The second
example is equivalent to @samp{centi * (meter^3)}, and gives a hundredth
of a cubic meter, not a cubic centimeter.  The @command{units} program
is limited internally to products of 99 units; accordingly, expressions
like @samp{meter^100} or @samp{joule^34} (represented internally as
@w{@samp{kg^34 m^68 / s^68}}) will fail.

The @samp{|}
operator has the highest precedence, so you can write the square root of
two thirds as @samp{2|3^1|2}.
The @samp{^} operator has the second highest precedence, and is
evaluated right to left, as usual:

@example
@group
You have: 5 * 2^3^2
You want:
        Definition: 2560
@end group
@end example

@noindent
With a dimensionless base unit, any dimensionless exponent is meaningful
(e.g., @samp{pi^exp(2.371)}).  Even though angle is sometimes treated as
dimensionless, exponents cannot have dimensions of angle:

@example
@group
You have: 2^radian
                 ^
Exponent not dimensionless
@end group
@end example

@noindent
If the base unit is not dimensionless, the
exponent must be a rational number @w{@var{p}/@var{q}}, and the
dimension of the unit must be a power of @var{q}, so @samp{gallon^2|3}
works but @samp{acre^2|3} fails.  An exponent using the slash (@samp{/})
operator (e.g., @samp{gallon^(2/3)}) is also acceptable; the parentheses
are needed because the precedence of @samp{^} is higher than that of
@samp{/}.  Since @command{units} cannot represent dimensions with
exponents greater than 99, a fully reduced exponent must have
@w{@var{q} < 100}.  When raising a non-dimensionless unit to a power,
@command{units} attempts to convert a decimal exponent to a rational
number with @w{@var{q} < 100}.  If this is not possible
@command{units} displays an error message:

@example
@group
You have: ft^1.234
Base unit not dimensionless; rational exponent required
@end group
@end example

@noindent
A decimal exponent must match its rational representation to machine
precision, so @samp{acre^1.5} works but @samp{gallon^0.666} does not.

@node Sums and Differences of Units
@c ---------------------------------------------------------------------
@section Sums and Differences of Units
@c ---------------------------------------------------------------------
@cindex sums and differences of units
@cindex units, sums and differences
@cindex operator, plus (@samp{+})
@cindex plus (@samp{+}) operator
@cindex @samp{+} operator
@cindex operator, minus (@samp{-})
@cindex minus (@samp{-}) operator, subtraction
@cindex operator, hyphen (@samp{-}) as subtraction
@cindex @samp{-} as subtraction operator

@noindent
You may sometimes want to add values of
different units that are outside the SI.
You may also wish to use @command{units} as a
calculator that keeps track of units.  Sums of conformable units are written with
the @samp{+} character, and differences with the @samp{-} character.
@cindex sums of units
@cindex addition of units
@cindex subtraction of units
@cindex differences of units

@example
@group
You have: 2 hours + 23 minutes + 32 seconds
You want: seconds
        * 8612
        / 0.00011611705
@end group
@end example


@example
@group
You have: 12 ft + 3 in
You want: cm
        * 373.38
        / 0.0026782366
@end group
@end example

@example
@group
You have: 2 btu + 450 ft lbf
You want: btu
        * 2.5782804
        / 0.38785542
@end group
@end example

@noindent
The expressions that are added or subtracted must reduce to identical
expressions in primitive units, or an error message will be displayed:

@example
@group
You have: 12 printerspoint - 4 heredium
                                      ^
Invalid sum of non-conformable units
@end group
@end example

@cindex parentheses
@noindent
If you add two values of vastly different scale you may exceed the
available precision of floating point (about 15 digits). The effect is
that the addition of the smaller value makes no change to the larger
value; in other words, the smaller value is treated as if it were zero.

@example
@group
You have: lightyear + cm
@end group
@end example

@noindent
No warning is given, however.
As usual, the precedence for @samp{+} and @samp{-} is lower than that of
the other operators.
A fractional quantity such as 2@tie{}1/2 cups can be given as
@samp{(2+1|2) cups}; the parentheses are necessary because
multiplication has higher precedence than addition.  If you omit the
parentheses, @command{units} attempts to add @samp{2} and
@samp{1|2 cups}, and you get an error message:

@example
@group
You have: 2+1|2 cups
                   ^
Invalid sum or difference of non-conformable units
@end group
@end example

@noindent
The expression could also be correctly written as @samp{(2+1/2) cups}.
If you write @samp{2@tie{}1|2 cups} the space is interpreted as
@emph{multiplication} so the result is the same as @samp{1 cup}.

The @samp{+} and @samp{-} characters sometimes appears in exponents like
@samp{3.43e+8}.  This leads to an ambiguity in an expression like
@samp{3e+2 yC}.  The unit @samp{e} is a small unit of charge, so this
can be regarded as equivalent to @samp{(3e+2) yC} or @samp{(3 e)+(2 yC)}.
This ambiguity is resolved by always interpreting @samp{+} and @samp{-} as part
of an exponent if possible.

@node Numbers as Units
@c ---------------------------------------------------------------------
@section Numbers as Units
@c ---------------------------------------------------------------------
@cindex numbers as units

For @command{units}, numbers are just another kind of unit.  They can
appear as many times as you like and in any order in a unit expression.
For example, to find the volume of a box that is 2 ft by 3 ft by 12 ft
in steres, you could do the following:

@example
@group
You have: 2 ft 3 ft 12 ft
You want: stere
        * 2.038813
        / 0.49048148

You have: $ 5 / yard
You want: cents / inch
        * 13.888889
        / 0.072
@end group
@end example
@noindent
And the second example shows how the dollar sign in the units conversion
can precede the five.  Be careful:  @command{units} will interpret
@samp{$5} with no space as equivalent to @samp{dollar^5}.

@node Built-in Functions
@c ---------------------------------------------------------------------
@section Built-in Functions
@c ---------------------------------------------------------------------
@cindex functions, built in
@cindex built-in functions

Several built-in functions are provided: @samp{sin}, @samp{cos}, @samp{tan},
@samp{secant}, @samp{csc}, @samp{cot},
@samp{asin}, @samp{acos}, @samp{atan},
@samp{asecant}, @samp{acsc}, @samp{acot}, 
@samp{sinh}, @samp{cosh}, @samp{tanh},
@samp{sech}, @samp{csch}, @samp{coth},
@samp{asinh}, @samp{acosh}, @samp{atanh},
@samp{asech}, @samp{acsch}, @samp{acoth},
@samp{exp}, @samp{ln}, @samp{log},
@samp{abs}, @samp{round}, @samp{floor}, @samp{ceil}, @samp{factorial},
@samp{Gamma}, @samp{lnGamma}, @samp{erf}, and @samp{erfc};
the function @samp{lnGamma} is the natural logarithm of the @samp{Gamma}
function.

The @samp{sin}, @samp{cos}, @samp{tan}, @samp{secant}, @samp{csc} and @samp{cot}
functions require either a dimensionless argument or an argument with
dimensions of angle.

@example
@group
You have: sin(30 degrees)
You want:
        Definition: 0.5

You have: sin(pi/2)
You want:
        Definition: 1

You have: sin(3 kg)
                  ^
Unit not dimensionless
@end group
@end example

@noindent
The other functions on the list require dimensionless arguments.  The
inverse trigonometric functions return arguments with dimensions of
angle.

@cindex logs
The @samp{ln} and @samp{log} functions give natural log and log base
10 respectively.  To obtain logs for any integer base, enter the
desired base immediately after @samp{log}.  For example, to get log
base 2 you would write @samp{log2} and to get log base 47 you could
write @samp{log47}.

@example
@group
You have: log2(32)
You want:
        Definition: 5
You have: log3(32)
You want:
        Definition: 3.1546488
You have: log4(32)
You want:
        Definition: 2.5
You have: log32(32)
You want:
        Definition: 1
You have: log(32)
You want:
        Definition: 1.50515
You have: log10(32)
You want:
        Definition: 1.50515
@end group
@end example

@cindex roots
@cindex square roots
If you wish to take roots of units, you may use the @samp{sqrt} or
@samp{cuberoot} functions.  These functions require that the argument
have the appropriate root.  You can obtain higher roots by using
fractional exponents:

@example
@group
You have: sqrt(acre)
You want: feet
        * 208.71074
        / 0.0047913202

You have: (400 W/m^2 / stefanboltzmann)^(1/4)
You have:
        Definition: 289.80882 K

You have: cuberoot(hectare)
                          ^
Unit not a root
@end group
@end example

@node Previous Result
@c ---------------------------------------------------------------------
@section Previous Result
@c ---------------------------------------------------------------------
@cindex previous result
@cindex @samp{_} to use result of previous conversion

@noindent
You can insert the result of the previous conversion using the
underscore (@samp{_}).  It is useful when you want to
convert the same input to several different units, for example

@example
@group
You have: 2.3 tonrefrigeration
You want: btu/hr
        * 27600
        / 3.6231884e-005
You have: _
You want: kW
        * 8.0887615
        / 0.12362832
@end group
@end example

@noindent
Suppose you want to do some deep frying that requires an oil depth of
2@tie{}inches.  You have 1/2 gallon of oil, and want to know the
largest-diameter pan that will maintain the required depth.  The
nonlinear unit @samp{circlearea} gives the @emph{radius} of the circle
(@pxref{Other Nonlinear Units}, for a more detailed description) in SI
units; you want the @emph{diameter} in @emph{inches}:

@example
@group
You have: 1|2 gallon / 2 in
You want: circlearea
        0.10890173 m
You have: 2 _
You want: in
        * 8.5749393
        / 0.1166189
@end group
@end example

@cindex white space

@noindent
In most cases, surrounding white space is optional, so the previous
example could have used @samp{2_}.  If @samp{_} follows a non-numerical
unit symbol, however, the space is required:

@example
@group
You have: m_
           ^
Parse error
@end group
@end example

@noindent
You can use the @samp{_} symbol any number of times; for example,

@example
@group
You have: m
You want:
        Definition: 1 m
You have: _ _
You want:
        Definition: 1 m^2
@end group
@end example

@noindent
Using @samp{_} before a conversion has been performed (e.g.,
immediately after invocation) generates an error:

@set codequoteundirected
@example
@group
You have: _
          ^
No previous result; '_' not set
@end group
@end example
@clear codequoteundirected

@noindent
Accordingly, @samp{_} serves no purpose when @command{units} is invoked
non-interactively.

If @command{units} is invoked with the @option{--verbose} option
(@pxref{Invoking Units}), the value of @samp{_} is not expanded:

@example
@group
You have: mile
You want: ft
        mile = 5280 ft
        mile = (1 / 0.00018939394) ft
You have: _
You want: m
        _ = 1609.344 m
        _ = (1 / 0.00062137119) m
@end group
@end example

@noindent
You can give @samp{_} at the @w{@samp{You want:}} prompt, but it
usually is not very useful.

@node Complicated Unit Expressions
@c ---------------------------------------------------------------------
@section Complicated Unit Expressions
@c ---------------------------------------------------------------------
@cindex unit expressions, complicated

@noindent
The @command{units} program is especially helpful in ensuring accuracy
and dimensional consistency when converting lengthy unit expressions.
@c noman
@cindex Darcy--Weisbach equation
For example, one form of the Darcy--Weisbach fluid-flow equation is
@c
@c ==================== Math for pressure drop example
@c ================
@ifnotinfo
@displaymath
 \Delta P = {8 \over \pi^2} \rho fL { Q^2 \over d^5}
@end displaymath
@end ifnotinfo
@ifinfo

@example
 Delta P = (8/pi^2) rho f L (Q^2 / d^5)
@end example

@end ifinfo
@noindent
@ifinfo
where @w{Delta P} is the pressure drop, rho
@end ifinfo
@ifnotinfo
where @math{ \Delta P} is the pressure drop, @math{\rho}
@end ifnotinfo
is the mass density,
@math{f} is the (dimensionless) friction factor, @math{L} is the length
of the pipe, @math{Q} is the volumetric flow rate, and @math{d}
is the pipe diameter.
You might want to have the equation in the form
@ifnotinfo
@displaymath
   \Delta P = A_1 \rho fL {Q^2 \over d^5}
@end displaymath
@end ifnotinfo
@ifinfo

@example
   Delta P = A1 rho f L (Q^2 / d^5)
@end example

@end ifinfo
@c end noman
@c -----------------------------------
@c nroff--assume neqn is not available
@c -----------------------------------
@c man .if t .ig ++
@c man For example, one form of the Darcy-Weisbach fluid-flow equation is
@c man .RS 5n
@c man .PP
@c man Delta \fIP\fP = (8 / pi)^2 (\fIrho\fP \fIfLQ\fP^2) / \fId\fP^5,
@c man .RE
@c man .PP
@c man where Delta \fIP\fP is the pressure drop, \fIrho\fP is the mass density,
@c man \fIf\fP is the (dimensionless) friction factor, \fIL\fP is the length
@c man of the pipe, \fIQ\fP is the volumetric flow rate, and \fId\fP
@c man is the pipe diameter.
@c man You might want to have the equation in the form
@c man .RS 5n
@c man .PP
@c man Delta \fIP\fP = A1 \fIrho\fP \fIfLQ\fP^2 / \fId\fP^5
@c man .RE
@c man .PP
@c man .++
@c -----
@c troff
@c -----
@c man .if n .ig ++
@c man .EQ
@c man delim $$
@c man .EN
@c don't assume en dash is available
@c man For example, one form of the Darcy\-Weisbach fluid-flow equation is
@c man .RS 5n
@c man .PP
@c man .EQ
@c man DELTA P = 8 over pi sup 2 rho fL Q sup 2 over d sup 5 ,
@c man .EN
@c man .RE
@c man .PP
@c man where $DELTA P$ is the pressure drop, $rho$ is the mass density,
@c man $f$ is the (dimensionless) friction factor, $L$ is the length
@c man of the pipe, $Q$ is the volumetric flow rate, and $d$
@c man is the pipe diameter.
@c man You might want to have the equation in the form
@c man .RS 5n
@c man .PP
@c man .EQ
@c man DELTA P = A sub 1 rho fL Q sup 2 over d sup 5
@c man .EN
@c man .RE
@c man .PP
@c man .EQ
@c man delim off
@c man .EN
@c man .++
@c ================ End Math for pressure drop example ================
@c
@noindent
that accepted the user's normal units; for typical units used in the US,
the required conversion could be something like

@example
@group
You have: (8/pi^2)(lbm/ft^3)ft(ft^3/s)^2(1/in^5)
You want: psi
        * 43.533969
        / 0.022970568
@end group
@end example

@cindex parentheses
@noindent
The parentheses allow individual terms in the expression to be entered naturally,
as they might be read from the formula.  Alternatively, the
multiplication could be done with the @samp{*} rather than a space;
then parentheses are needed only around @samp{ft^3/s} because of its
exponent:

@example
@group
You have: 8/pi^2 * lbm/ft^3 * ft * (ft^3/s)^2 /in^5
You want: psi
        * 43.533969
        / 0.022970568
@end group
@end example

@noindent
Without parentheses, and using spaces for multiplication, the previous
conversion would need to be entered as

@example
@group
You have: 8 lb ft ft^3 ft^3 / pi^2 ft^3 s^2 in^5
You want: psi
        * 43.533969
        / 0.022970568
@end group
@end example

@node Variables Assigned at Run Time
@c ---------------------------------------------------------------------
@section Variables Assigned at Run Time
@c ---------------------------------------------------------------------
@cindex variables assigned at run time
@cindex runtime variables
@cindex @samp{=} operator
@cindex operator, @samp{=}

Unit definitions are fixed once @command{units} has finished reading the
units data file(s), but at run time you can assign unit expressions to
variables whose names begin with an underscore, using the syntax

@example
_@var{name} = @var{<unit expression>}
@end example

@noindent
This can help manage a long calculation by saving intermediate
quantities as variables that you can use later.  For example, to
determine the shot-noise-limited signal-to-noise ratio (SNR) of an
imaging system using a helium--neon laser, you could do

@example
You have: _lambda = 632.8 nm            # laser wavelength
You have: _nu = c / _lambda             # optical frequency
You have: _photon_energy = h * _nu
You have: _power = 550 uW
You have: _photon_count = _power * 500 ns / _photon_energy
You have: _snr = sqrt(_photon_count)
You have: _snr
You want:
        Definition: sqrt(_photon_count) = 29597.922
@end example

@noindent
Except for beginning with an underscore, runtime variables follow the
same naming rules as units.  Because names beginning with @samp{_} are
reserved for these variables and unit names cannot begin with @samp{_},
runtime variables can never hide unit definitions.  Runtime variables
are undefined until you make an assignment to them, so if you give a
name beginning with an underscore and no assignment has been made, you
get an error message.

When you assign a unit expression to a runtime variable, @command{units}
checks the expression to determine whether it is valid, but the
resulting definition is stored as a text string that is not reduced to
primitive units.  The text will be processed anew each time you use the
variable in a conversion or calculation;  this means that if your
definition depends on other runtime variables (or the special variable
@samp{_}), the result of calculating with your variable will change if
any of those variables change.  A dependence need not be direct.

Continuing the example of the laser above, suppose you have done the
calculation as shown.  You now wonder what happens if you switch to an
argon laser:

@example
@group
You have: _lambda = 454.6 nm
You have: _snr
You want:
        Definition: sqrt(_photon_count) = 25086.651
@end group
@end example

@noindent
If you then change the power:

@example
@group
You have: _power = 1 mW
You have: _snr
You want:
        Definition: sqrt(_photon_count) = 33826.834
@end group
@end example

@noindent
Instead of having to reenter or edit a lengthy expression when you
perform another calculation, you need only enter values that change; in
this respect, runtime variables are similar to a spreadsheet.

The more times a variable appears in an expression that depends on it,
the greater the benefit of having a calculation using that expression
reflect changes to that variable.  For example, the length of
daylight---the time the Sun is above the horizon---at a given latitude
and declination of the Sun is given by

@c ================ Math for day length example ==========================
@c noman
@ifnotinfo
@displaymath
  L = 2 \cos^{-1} \left (
    { \sin h  - \sin \phi \sin \delta  }
      \over
    { \cos \phi \cos \delta  }
  \right )
@end displaymath
@end ifnotinfo

@ifinfo
L = 2 acos((sin(h) - cos(phi) cos (delta)) / (cos(phi) cos(delta)))

@end ifinfo
@noindent
where @math{L} is the day length, @math{h} is the Sun's altitude
(elevation angle), @math{\phi} is the location's latitude, and
@math{\delta} is the Sun's declination (angle with the equatorial plane).
@c end noman
@c -----------------------------------
@c nroff--assume neqn is not available
@c -----------------------------------
@c man .if t .ig ++
@c man .RS 5n
@c man .PP
@c man \fIL\fP = acos((sin \fIh\fP - sin \fI\(*f\fP sin \fI\(*d\fP) /
@c man                (cos \fI\(*f\fP cos \fI\(*d\fP))
@c man .RE
@c man .PP
@c man where \fIL\fP is the day length, \fIh\fP is the altitude,
@c man \fI\(*f\fP is the latitude, and \fI\(*d\fP is the Sun's declination.
@c man .++
@c -----
@c troff
@c -----
@c man .if n .ig ++
@c man .EQ
@c man delim $$
@c man .EN
@c man .RS 5n
@c man .PP
@c man .EQ
@c man L = 2 cos sup {-1} left (
@c man             {sin h - sin phi sin delta}
@c man               over
@c man             {cos phi cos delta}
@c man           right )
@c man .EN
@c man .RE
@c man .PP
@c man where $L$ is the day length, $phi$ is the latitude, and $delta$
@c man is the Sun's declination.
@c man .EQ
@c man delim off
@c man .EN
@c man .++
@c
@c ============= End Math for day length example =======================
@c
The result above is in sidereal time; the length in solar time is
obtained by multiplying by

@example
siderealday / day
@end example

@noindent
By convention, the Sun's altitude at rise or set is
@c noman
@ifnotinfo
@math{-50^\prime}
@end ifnotinfo
@ifinfo
-50'
@end ifinfo
@c end noman
@ignore
@c ifman
\&\-50\(fm
@c end ifman
@end ignore
to allow for atmospheric refraction and the semidiameter of its disk.
At the summer solstice in the northern hemisphere, the Sun's declination
is approximately
@ifinfo
23.44@textdegree{};
@end ifinfo
@ifnotinfo
@math{23.44^\circ};
@end ifnotinfo
to find the length of the longest day of the year
for a latitude of
@ifnotinfo
@math{55^\circ},
@end ifnotinfo
@ifinfo
55@textdegree{};
@end ifinfo
you could do

@example
@group
You have: _alt = -50 arcmin
You have: _lat = 55 deg
You have: _decl = 23.44 deg
You have: _num = sin(_alt) - sin(_lat) sin(_decl)
You have: _denom = cos(_lat) cos(_decl)
You have: _sday = 2 (acos(_num / _denom) / circle) 24 hr
You have: _day = _sday siderealday / day
You have: _day
You want: hms
        17 hr + 19 min + 34.895151 sec
@end group
@end example

@noindent
At the winter solstice, the Sun's declination is approximately
@ifnotinfo
@math{-23.44^\circ},
@end ifnotinfo
@ifinfo
-23.44@textdegree{};
@end ifinfo
so you could calculate
the length of the shortest day of
the year using:

@example
@group
You have: _decl = -23.44 deg
You have: _day
You want: hms
        7 hr + 8 min + 40.981084 sec
@end group
@end example

@noindent
Latitude and declination each appear twice in the expression for
@code{_day}; the result in the examples above is updated by changing
only the value of the declination.

It may seem easier---and less subject to error---to simply specify the
new value of @code{_decl} as the negative of the current value (e.g.,
@w{@samp{_decl = -_decl}}).  This doesn't work; when you make an
assignment with the @samp{=} operator, the definition is stored as
entered, including possible dependencies on variables.  But if you
attempt an assignment that is ultimately self-referential, the current
definition is retained, and you get an error message.  For example,
@cindex @samp{=} operator
@cindex operator, @samp{=}

@example
@group
You have: _decl = 23.44 deg
You have: _decl = -_decl
Circular unit definition
@end group
@end example

@noindent
You can overcome this by using the @samp{:=} operator, which reduces the
right hand side to primitive units before making the assignment,
eliminating any dependencies on variables.  Returning to the example
above,
@cindex @samp{:=} operator
@cindex operator, @samp{:=}

@example
@group
You have: _decl = 23.44 deg
You have: _decl = -_decl
Circular unit definition
You have: _decl := -_decl
You have: _decl
You want: deg
        * -23.44
        / -0.042662116
@end group
@end example

@noindent
This works to much the same effect as if the assignment had been
entered literally, e.g.,

@example
You have: _decl = -23.44 deg
@end example

@noindent
but the actual definition is in primitive units---in this case,
radians:

@example
@group
You have: _decl = 23.44 deg
You have: _decl := -_decl
You have: _decl
You want:
        Definition: -0.40910517666747087 radian = -0.40910518 radian
@end group
@end example

@noindent
Definitions are text strings, and a redefinition using @samp{:=} is given
with enough digits maintain the full precision of the current definition
when converted back to a number; because it is a string, all digits are
displayed when showing the definition, regardless of the numerical
display precision, so you may see more digits than expected.

A runtime variable must be assigned before it can be used in an
assignment; in the first of the three examples above, giving the general
equation before the values for @code{_alt}, @code{_lat}, and @code{_decl}
had been assigned would result in an error message.

You can display a list of runtime variables you have assigned by typing
@w{@kbd{search _}}.

@node Backwards Compatibility
@c ---------------------------------------------------------------------
@section Backwards Compatibility: @samp{*} and @samp{-}
@c ---------------------------------------------------------------------
@cindex backwards compatibility
@cindex compatibility
@cindex compatibility with earlier versions

The original @command{units} assigned multiplication a higher
precedence than division using the slash.  This differs from the
usual precedence rules, which give multiplication and division equal
precedence, and can be confusing for people who think
of units as a calculator.

The star operator (@samp{*}) included in this @command{units} program
has, by default, the same precedence as division,
and hence follows the usual precedence rules.  For backwards
compatibility you can invoke @command{units}
with the @option{--oldstar}
option.  Then @samp{*} has a higher precedence than
division, and the same precedence as multiplication using the space.

@cindex @samp{-} as multiplication operator
@cindex operator, hyphen (@samp{-}) as multiplication
@cindex multiplication, hyphen
@cindex hyphen as multiplication operator

Historically, the hyphen (@samp{-}) has been used in technical
publications to indicate products of units, and the original
@command{units} program treated it as a multiplication operator.
Because @command{units} provides
several other ways to obtain unit products, and because @samp{-} is a
subtraction operator in general algebraic expressions, @command{units}
treats the binary @samp{-} as a subtraction operator by default.
For backwards compatibility use the @option{--product} option, which
causes @command{units} to treat the binary @samp{-} operator as a
product operator.  When @samp{-} is a multiplication operator
it has the same precedence as multiplication with a space, giving it a
higher precedence than division.

When @samp{-} is used as a unary operator it negates its operand.
Regardless of the @command{units} options, if
@samp{-} appears after @samp{(} or after
@samp{+}, then it will act as a negation operator.  So you can always compute 20
degrees minus 12 minutes by entering @samp{20@tie{}degrees + -12@tie{}arcmin}.
You must use this construction when you define new units because you
cannot know what options will be in force when your definition is
processed.
@cindex defining units with `-'

@node Nonlinear Conversions
@c =====================================================================
@chapter Nonlinear Unit Conversions
@c =====================================================================
@cindex nonlinear unit conversions

Nonlinear units are represented using functional notation.  They make
possible nonlinear unit conversions such as temperature.

@menu
* Temperature Conversions::  Conversion between temperature scales
* US Consumer Price Index::  US Consumer Price Index
* Other Nonlinear Units::    Ring size, wire gauge, abrasive grit size
* Multivariate Functions::   Multivariate functions: hypot, wind chill
@end menu

@node Temperature Conversions
@c ---------------------------------------------------------------------
@section Temperature Conversions
@c ---------------------------------------------------------------------
@cindex temperature conversions

Conversions between temperatures are different from linear conversions
between temperature @emph{increments}---see the example below.  The
absolute temperature conversions are handled by units starting with
@samp{temp}, and you must use functional notation.
The temperature-increment conversions are done using units starting
with @samp{deg} and they do not require functional notation.

@example
@group
You have: tempF(45)
You want: tempC
        7.2222222

You have: 45 degF
You want: degC
        * 25
        / 0.04
@end group
@end example

@noindent
Think of @samp{tempF(@var{x})} not as a function but as a notation that
indicates that @var{x} should have units of @samp{tempF} attached to
it.  @xref{Defining Nonlinear Units}.  The first conversion shows that if it's 45
degrees Fahrenheit outside, it's 7.2 degrees Celsius.  The second
conversion indicates that a change of 45 degrees Fahrenheit corresponds
to a change of 25 degrees Celsius.  The conversion from
@samp{tempF(@var{x})} is to absolute temperature, so that

@example
@group
You have: tempF(45)
You want: degR
        * 504.67
        / 0.0019814929
@end group
@end example

@noindent
gives the same result as

@example
@group
You have: tempF(45)
You want: tempR
        * 504.67
        / 0.0019814929
@end group
@end example

@noindent
But if you convert @samp{tempF(@var{x})} to @samp{degC}, the output is
probably not what you expect:

@example
@group
You have: tempF(45)
You want: degC
        * 280.37222
        / 0.0035666871
@end group
@end example

@noindent
The result is the temperature in K, because @samp{degC} is defined as
@samp{K}, the kelvin. For consistent results, use the @samp{temp@var{X}} units
when converting to a temperature rather than converting a temperature
increment.

The @samp{tempC()} and @samp{tempF()} definitions are limited to
positive absolute temperatures, and giving a value that would result in
a negative absolute temperature generates an error message:

@example
@group
You have: tempC(-275)
                    ^
Argument of function outside domain
@end group
@end example

@node US Consumer Price Index
@c ---------------------------------------------------------------------
@section US Consumer Price Index
@c ---------------------------------------------------------------------
@cindex US Consumer Price Index
@cindex Consumer Price Index
@cindex CPI

@command{units} includes the US Consumer Price Index published by the US
Bureau of Labor Statistics.  Several functions that use this value are
provided:
@samp{cpi},
@samp{cpi_now},
@samp{inflation_since},
and
@samp{dollars_in}.

The @samp{cpi} function gives the CPI for a specified decimal year.  A
@dfn{decimal year} is given as the year plus the fractional part of the
year; because of leap years and the different lengths of months,
calculating an exact value for the fractional part can be tedious, but
for the purposes of CPI, an approximate value is usually 
adequate.  For example, @w{1 January} 2000 is 2000.0, @w{1 April} 2000 is 2000.25,
@w{1 July} 2000 is 2000.4986, and @w{1 October} 2000 is 2000.75.
Note also that the CPI data update monthly; values in between months
are linearly interpolated.  

In the middle of 1975, the CPI was

@example
@group
You have: cpi(1975.5)
You want:
        Definition: 53.6
@end group
@end example

@noindent
The value of the CPI for a month is usually published sometime around
the 20th day of the following month; the latest value of the CPI is available with
@samp{cpi_now}.  On @w{7 January} 2024, the value was

@example
@group
You have: cpi_now
You want:
        Definition: UScpi_now = 307.051
@end group
@end example

@noindent
This means that the CPI was 307.015 on @w{1 December} 2023.  The
@samp{cpi_now} variable can only present the most recent data available,
so it can lag the current CPI by several weeks.
The decimal year of the last update is available with @samp{cpi_lastdate}.

The @samp{inflation_since} function provides a convenient way to
determine the inflation factor from a specified decimal year to the
latest value in the CPI table.  For example, on @w{7 January} 2024:

@example
@group
You have: inflation_since(1970)
You want:
        Definition: 8.1445889
@end group
@end example

@noindent
In other words, goods that cost 1 US$ in 1970 would cost 8.14 US$ on
@w{1 December} 2023.

The @samp{inflation_since} function can be used to determine an annual
rate of inflation.  The earliest US CPI data are from about 1913.1; the
approximate time between then and @w{7 January} 2024 is 110.9 years.  The
approximate annual inflation rate for that period is then

@example
@group
You have: inflation_since(1913.1)^1|110.9 - 1
You want: %
        * 3.1548115
        / 0.31697614
@end group
@end example

@noindent
The inflation rate for any time period can be found from the ratio of
the CPI at the end of the period to that of the beginning:

@example
@group
You have: (cpi(1982)/cpi(1972))^1|10 - 1
You want: %
        * 8.6247033
        / 0.11594602
@end group
@end example

@noindent
The period 1972--1982 was indeed one of high inflation.

The @samp{dollars_in} function is similar to @samp{inflation_since} but
its output is in US$ rather than dimensionless:

@example
@group
You have: dollars_in(1970)
You want:
        Definition: 8.1445889 US$
@end group
@end example

@noindent
A typical use might be

@example
@group
You have: 250 dollars_in(1970)
You want: $
        * 2036.1472
        / 0.00049112362
@end group
@end example

@noindent
Because @samp{dollars_in} includes the units, you should not
include them at the @w{@samp{You have:}} prompt.  You can also
use @samp{dollars_in} to convert between two specified years:

@example
@group
You have: 250 dollars_in(1970)
You want: dollars_in(1950)
        * 156.49867
        / 0.0063898305
@end group
@end example

@noindent
which shows that 250 US$ in 1970 would have equivalent purchasing
power to 156 US$ in 1950.  

@node Other Nonlinear Units
@c ---------------------------------------------------------------------
@section Other Nonlinear Units
@c ---------------------------------------------------------------------
@cindex nonlinear units, other

Some other examples of nonlinear units are numerous different ring sizes
and wire gauges, screw gauges, pipe and tubing sizes, the grit sizes
used for abrasives, the decibel scale, shoe size, scales for the density
of sugar (e.g., baume).  The standard data file also supplies units for
computing the area of a circle and the volume of a sphere.  See the
standard units data file for more details.
@cindex wire gauge
@cindex wire size
@cindex American Wire Gauge (AWG)

Diameters of American wire sizes can be found using the
@samp{wiregauge()} function or its alias @samp{awg()}:

@example
@group
You have: wiregauge(11)
You want: inches
        * 0.090742002
        / 11.020255

You have: 1 mm
You want: wiregauge
        18.201919
@end group
@end example

@noindent
Wire and screw gauges with multiple zeroes are signified using negative
numbers, where two zeroes (``00''; ``2/0'') is @samp{-1}, three zeros
(``000''; ``3/0'') is @samp{-2}, and so on.  Alternatively, you can use
the synonyms @samp{g00}, @samp{g000}, or @samp{g2_0}, @samp{g3_0}, and
so on that are defined in the standard units data file.

@example
@group
You have: brwiregauge(g00)
You want: inches
        * 0.348
        / 2.8735632
@end group
@end example

@noindent
In North America, wire sizes larger than 0000 (``4/0'') are usually
given in terms of area, either in kcmil or the older initialism MCM
(thousand circular mils).  Outside of North America, all wire sizes are
usually given in terms of area in
@c noman
@ifinfo
mm^2.
@end ifinfo
@c
@ifnotinfo
mm@sup{2}.
@end ifnotinfo
@c end noman
@c man .if n mm^2.
@c man .if t mm\v'-.4m'\s-32\s0\v'.4m'.
@c mm@sup{2}.
Wire area can be
obtained using @samp{wiregaugeA()} or its alias @samp{awgA()}:

@example
@group
You have: awgA(g6_0)
You want: kcmil
        * 336.45718
        / 0.0029721464
You have: awgA(12)
You want: mm^2
        * 3.3087729
        / 0.30222685
@end group
@end example

@noindent
The closest standard metric sizes are
2.5@tie{}mm@sup{2} and 4@tie{}mm@sup{2}; in general, there isn't an
exact correlation between American and metric wire sizes.

@cindex iron pipe size (IPS)
@cindex nominal pipe size (NPS)
@cindex pipe size
Though based on the long-established iron pipe size (IPS) given in
inches, nominal pipe size (NPS) is a dimensionless quantity that
corresponds to the inch size.  Pipe size can be equivalently specified
using metric diam@U{00E8}tre nominal (DN), which roughly corresponds to
the diameter in mm.  For a given pipe size, outside diameter is constant
while inside diameter varies with schedule.  For example, for NPS
2@U{00BD} pipe,

@example
@group
You have: npsOD(2+1|2)
You want: in
        * 2.875
        / 0.34782609
You have: nps40(2+1|2)
You want: in
        * 2.469
        / 0.40502228
You have: nps80(2+1|2)
You want: in
        * 2.323
        / 0.43047783
@end group
@end example

@noindent
Pipe size can be given equivalently in terms of the metric DN by using
the @samp{DN()} function, which converts nominal metric size to nominal
inch size:

@example
@group
You have: npsOD(DN(65))
You want: mm
        * 73.025
        / 0.01369394
You have: _
You want: in
        * 2.875
        / 0.34782609
@end group
@end example

@noindent
Unlike with wire sizes, actual NPS and metric DN pipe dimensions are the
same.

@example
@group
You have: grit_P(600)
You want: grit_ansicoated
        342.76923
@end group
@end example

@noindent
The last example shows the conversion from P graded sand paper,
which is the European standard and may be marked ``P600'' on the back,
to the USA standard.
@cindex abrasive grit size

You can compute the area of a circle using the nonlinear unit,
@samp{circlearea}.  You can also do this using the circularinch or
circleinch.  The next example shows two ways to compute the area of a
circle with a five inch radius and one way to compute the volume of a
sphere with a radius of one meter.
@cindex circle, area of
@cindex sphere, volume of

@example
@group
You have: circlearea(5 in)
You want: in2
        * 78.539816
        / 0.012732395

You have: 10^2 circleinch
You want: in2
        * 78.539816
        / 0.012732395

You have: spherevol(meter)
You want: ft3
        * 147.92573
        / 0.0067601492
@end group
@end example

@noindent
The inverse of a nonlinear conversion is indicated by prefixing a tilde
(@samp{~}) to the nonlinear unit name:

@example
@group
You have: ~wiregauge(0.090742002 inches)
You want:
        Definition: 11
@end group
@end example

@noindent
You can give a nonlinear unit definition without an argument or
parentheses, and press @key{Enter} at the @w{@samp{You want:}} prompt to
get the definition of a nonlinear unit; if the definition is not valid
for all real numbers, the range of validity is also given.  If the
definition requires specific units this information is also
displayed:

@example
@group
You have: tempC
        Definition: tempC(x) = x K + stdtemp
                    defined for x >= -273.15
You have: ~tempC
        Definition: ~tempC(tempC) = (tempC +(-stdtemp))/K
                    defined for tempC >= 0 K
You have: circlearea
        Definition: circlearea(r) = pi r^2
                    r has units m
@end group
@end example

@noindent
To see the definition of the inverse use the @samp{~} notation.  In
this case the parameter in the functional definition will
usually be the name of the unit.  Note that the inverse for
@samp{tempC} shows that it requires units of @samp{K} in the
specification of the allowed range of values.
Nonlinear unit conversions are described in more detail in
@ref{Defining Nonlinear Units}.


@node Multivariate Functions
@c ---------------------------------------------------------------------
@section Multivariate Functions
@c ---------------------------------------------------------------------
@cindex multivariate functions

The @command{units} program supports some multivariate functions for performing calculations with
units.  The @samp{hypot} function computes the length of a hypotenuse given
two sides.  It works with any pair of values that have compatible dimensions.  

@example
@group
You have: hypot(3 m, 4 m)
You want: 
        Definition: 5 m
@end group
@end example

You can compute wind chill, based on temperature and wind speed, or heat index,
based on temperature and humidity, with humidity given as a fraction,
e.g., 0.5 for a 50% relative humidity.

@example
@group
You have: windchill(tempF(28), 14 mph)
You want: tempF
        16.86826
You have: heatindex(tempC(40),0.5)
You want: tempC
        54.767952
@end group        
@end example

Both wind chill and heat index return a value that is nominally a temperature,
so you will want to convert it to Fahrenheit or Celsius as shown in
order to get a meaningful numerical value.  

@node Unit Lists
@c =====================================================================
@chapter Unit Lists: Conversion to Sums of Units
@c =====================================================================
@cindex sums of units
@cindex unit lists
@cindex units, sums of

@menu
* Cooking Measure
* Unit List Aliases
@end menu

Outside of the SI, it is sometimes desirable to convert a single
unit to a sum of units---for example, feet to feet plus inches.
The conversion @emph{from} sums of units was described in
@ref{Sums and Differences of Units}, and is a simple matter of adding
the units with the @samp{+} sign:

@example
@group
You have: 12 ft + 3 in + 3|8 in
You want: ft
        * 12.28125
        / 0.081424936
@end group
@end example

@noindent
Although you can similarly write a sum of units to convert @emph{to},
the result will not be the conversion to the units in the sum, but
rather the conversion to the particular sum that you have entered:

@example
@group
You have: 12.28125 ft
You want: ft + in + 1|8 in
        * 11.228571
        / 0.089058524
@end group
@end example

@noindent
The unit expression given at the @w{@samp{You want:}} prompt is
equivalent to asking for conversion to multiples of
@samp{1@tie{}ft + 1@tie{}in + 1|8@tie{}in}, which is 1.09375 ft, so the
conversion in the previous example is equivalent to

@example
@group
You have: 12.28125 ft
You want: 1.09375 ft
        * 11.228571
        / 0.089058524
@end group
@end example

@noindent
In converting to a sum of units like miles, feet and inches, you
typically want the largest integral value for the first unit, followed
by the largest integral value for the next, and the remainder converted
to the last unit.
You can do this conversion easily with @command{units} using a special
syntax for lists of units.  You must list the desired units in order
from largest to smallest, separated by the semicolon (@samp{;})
character:

@example
@group
You have: 12.28125 ft
You want: ft;in;1|8 in
        12 ft + 3 in + 3|8 in
@end group
@end example

@noindent
The conversion always gives integer coefficients on the units in the
list, except possibly the last unit when the conversion is not exact:

@example
@group
You have: 12.28126 ft
You want: ft;in;1|8 in
        12 ft + 3 in + 3.00096 * 1|8 in
@end group
@end example

@noindent
The order in which you list the units is important:

@example
@group
You have: 3 kg
You want: oz;lb
        105 oz + 0.051367866 lb

You have: 3 kg
You want: lb;oz
        6 lb + 9.8218858 oz
@end group
@end example

@noindent
Listing ounces before pounds produces a technically correct result,
but not a very useful one.  You must list the units in descending
order of size in order to get the most useful result.

Ending a unit list with the separator @samp{;}
has the same effect as repeating the last
unit on the list, so @samp{ft;in;1|8 in;} is equivalent to
@samp{ft;in;1|8 in;1|8 in}.  With the example above, this gives

@example
@group
You have: 12.28126 ft
You want: ft;in;1|8 in;
        12 ft + 3 in + 3|8 in + 0.00096 * 1|8 in
@end group
@end example

@noindent
in effect separating the integer and fractional parts of the
coefficient for the last unit.  If you instead
prefer to round the last coefficient to an integer
you can do this with the @option{--round} (@option{-r}) option.
With the previous example, the result is

@example
@group
You have: 12.28126 ft
You want: ft;in;1|8 in
        12 ft + 3 in + 3|8 in (rounded down to nearest 1|8 in)
@end group
@end example

@noindent
When you use the @option{-r} option, repeating the last unit on the
list has no effect (e.g., @samp{ft;in;1|8 in;1|8 in} is equivalent to
@samp{ft;in;1|8 in}), and hence neither does ending a list with a
@samp{;}.  With a single unit and the @option{-r} option, a terminal @samp{;}
@emph{does} have an effect: it causes @command{units} to treat the
single unit as a list and produce a rounded value for the single unit.
Without the extra @samp{;}, the @option{-r} option has no effect on
single unit conversions.  This example shows the output using the
@option{-r} option:

@example
@group
You have: 12.28126 ft
You want: in
        * 147.37512
        / 0.0067854058

You have: 12.28126 ft
You want: in;
        147 in (rounded down to nearest in)
@end group
@end example

@noindent
Each unit that appears in the list must be conformable with the first
unit on the list, and of course the listed units must also be
conformable with the unit that you enter at the @w{@samp{You have:}}
prompt.

@example
@group
You have: meter
You want: ft;kg
             ^
conformability error
        ft = 0.3048 m
        kg = 1 kg

You have: meter
You want: lb;oz
conformability error
        1 m
        0.45359237 kg
@end group
@end example

@noindent
In the first case, @command{units} reports the disagreement between
units appearing on the list.  In the second case, @command{units}
reports disagreement between the unit you entered and the desired
conversion.  This conformability error is based on the first
unit on the unit list.

Other common candidates for conversion to sums of units are
angles and time:

@example
@group
You have: 23.437754 deg
You want: deg;arcmin;arcsec
    23 deg + 26 arcmin + 15.9144 arcsec

You have: 7.2319 hr
You want: hr;min;sec
    7 hr + 13 min + 54.84 sec
@end group
@end example

@noindent
Some applications for unit lists may be less obvious.  Suppose that you
have a postal scale and wish to ensure that it's accurate at 1@tie{}oz,
but have only metric calibration weights.  You might try

@example
@group
You have: 1 oz
You want: 100 g;50 g; 20 g;10 g;5 g;2 g;1 g;
        20 g + 5 g + 2 g + 1 g + 0.34952312 * 1 g
@end group
@end example

@noindent
You might then place one each of the 20@tie{}g, 5@tie{}g, 2@tie{}g, and
1@tie{}g weights on the scale and hope that it indicates close to

@example
@group
You have: 20 g + 5 g + 2 g + 1 g
You want: oz;
        0.98767093 oz
@end group
@end example

@noindent
Appending @samp{;} to @samp{oz} forces a one-line display that includes
the unit; here the integer part of the result is zero, so it is not
displayed.

If a non-empty list item differs vastly in scale from the quantity from
which the list is to be converted, you may exceed the available
precision of floating point (about 15 digits), in which case you will
get a warning, e.g.,

@example
@group
You have: lightyear
You want: mile;100 inch;10 inch;mm;micron
        5.8786254e+12 mile + 390 * 100 inch (at 15-digit precision limit)
@end group
@end example


@c ---------------------------------------------------------------------
@section Cooking Measure
@c ---------------------------------------------------------------------

@noindent
In North America, recipes for cooking typically measure ingredients by
volume, and use units that are not always convenient multiples of each
other.  Suppose that you have a recipe for 6 and you wish to make a
portion for 1.  If the recipe calls for 2@tie{}1/2 cups of an
ingredient, you might wish to know the measurements in terms of
measuring devices you have available, you could use @command{units} and
enter

@example
@group
You have: (2+1|2) cup / 6
You want: cup;1|2 cup;1|3 cup;1|4 cup;tbsp;tsp;1|2 tsp;1|4 tsp
        1|3 cup + 1 tbsp + 1 tsp
@end group
@end example

@noindent
By default, if a unit in a list begins with fraction of the form
1|@var{x} and its multiplier is an integer, the fraction is given as
the product of the multiplier and the numerator; for example,

@example
@group
You have: 12.28125 ft
You want: ft;in;1|8 in;
        12 ft + 3 in + 3|8 in
@end group
@end example

@noindent
In many cases, such as the example above, this is what is wanted, but
sometimes it is not.  For example, a cooking recipe for 6 might call
for 5@tie{}1/4 cup of an ingredient, but you want a portion for 2, and
your 1-cup measure is not available; you might try

@example
@group
You have: (5+1|4) cup / 3
You want: 1|2 cup;1|3 cup;1|4 cup
        3|2 cup + 1|4 cup
@end group
@end example

@noindent
This result might be fine for a baker who has a 1@tie{}1/2-cup measure
(and recognizes the equivalence), but it may not be as useful to
someone with more limited set of measures, who does want to do
additional calculations, and only wants to know ``How many 1/2-cup
measures to I need to add?''  After all, that's what was actually
asked.  With the @option{--show-factor} option, the factor will not be
combined with a unity numerator, so that you get

@example
@group
You have: (5+1|4) cup / 3
You want: 1|2 cup;1|3 cup;1|4 cup
        3 * 1|2 cup + 1|4 cup
@end group
@end example

@noindent
A user-specified fractional unit with a numerator other than 1 is never
overridden, however---if a unit list specifies @samp{3|4 cup;1|2 cup},
a result equivalent to 1@tie{}1/2 cups will always be shown as
@samp{2 * 3|4@tie{}cup} whether or not the @option{--show-factor} option
is given.


@c ---------------------------------------------------------------------
@section Unit List Aliases
@c ---------------------------------------------------------------------
@cindex unit list aliases

@noindent
A unit list such as

@example
cup;1|2@tie{}cup;1|3@tie{}cup;1|4@tie{}cup;tbsp;tsp;1|2@tie{}tsp;1|4@tie{}tsp
@end example

@noindent
can be tedious to enter.  The @command{units} program provides shorthand names
for some common combinations:

@example
hms         @r{time: hours, minutes, seconds}
dms         @r{angle: degrees, minutes, seconds}
time        @r{time: years, days, hours, minutes and seconds}
usvol       @r{US cooking volume: cups and smaller}
uswt        @r{US weight: pounds and ounces}
ftin        @r{length: feet, inches and 1/8 inches}
ftin2       @r{length: feet, inches and 1/2 inches}
ftin4       @r{length: feet, inches and 1/4 inches}
ftin8       @r{length: feet, inches and 1/8 inches}
ftin16      @r{length: feet, inches and 1/16 inches}
ftin32      @r{length: feet, inches and 1/32 inches}
ftin64      @r{length: feet, inches and 1/64 inches}
inchfine    @r{length: inches subdivided to 1/64 inch}
@end example

@noindent
Using these shorthands, or @dfn{unit list aliases},
you can do the following conversions:

@example
@group
You have: anomalisticyear
You want: time
        1 year + 25 min + 3.4653216 sec
You have: 1|6 cup
You want: usvol
        2 tbsp + 2 tsp
@end group
@end example

@noindent
Suppose you want to drill a clearance hole for a #10 screw and have
about 1/64 inch clearance; you could try

@example
@group
You have: screwgauge(10) + 1|64 in
You want: ftin64
        13.16 * 1|64 in
You have: _
You want: ftin32
        6.58 * 1|32 in
@end group
@end example

@noindent
If a slightly tight fit is acceptable, a 13/64-inch drill would do the
job; if not, a 7/32-inch drill would work with a slightly looser fit.

You can define your own unit list aliases;
@pxref{Defining Unit List Aliases}.

You cannot combine a unit list alias with other units: it must appear
alone at the @w{@samp{You want:}} prompt.

You can display the definition of a unit list alias by entering it at
the @w{@samp{You have:}} prompt:

@example
@group
You have: dms
        Definition: unit list, deg;arcmin;arcsec
@end group
@end example

@noindent
When you specify compact output with @option{--compact},
@option{--terse} or @option{-t} and perform conversion to a unit list,
@command{units} lists the conversion factors for each unit in the
list, separated by semicolons.

@example
@group
You have: year
You want: day;min;sec
365;348;45.974678
@end group
@end example

@noindent
Unlike the case of regular
output, zeros @emph{are} included in this output list:

@example
@group
You have: liter
You want: cup;1|2 cup;1|4 cup;tbsp
4;0;0;3.6280454
@end group
@end example

@node Alternative Unit Systems
@c =====================================================================
@chapter Alternative Unit Systems
@c =====================================================================

@menu
* CGS Units::
* Natural Units::
* Prompt Prefix::              The prompt prefix shows specified CGS units
@end menu

@node CGS Units
@c ---------------------------------------------------------------------
@section CGS Units
@c ---------------------------------------------------------------------
@cindex CGS units, using



@menu
* Specifying CGS Units::       How to specify the desired CGS units
* CGS Units Systems::          The various CGS units systems
* Conversions Between Systems:: Conversions between units in different systems
@end menu

The SI---an extension of the MKS (meter--kilogram--second) system---has
largely supplanted the older CGS (centimeter--gram--second) system, but
CGS units are still used in a few specialized fields, especially in
physics where they lead to a more elegant formulation of Maxwell's equations.
Conversions between SI and CGS involving mechanical units are
straightforward, involving powers of 10 (e.g., @w{1 m = 100 cm}).
Conversions involving electromagnetic units are more complicated, and
@command{units} supports four different systems of CGS units:
electrostatic units (ESU), electromagnetic units (EMU), the
Gaussian system and the Heaviside--Lorentz system.
The differences between these systems
arise from different choices made for proportionality
constants in electromagnetic equations.
Coulomb's law gives electrostatic force between two
charges separated by a distance
@c noman
@math{r}:
@ifinfo
@display

F = k_C q_1 q_2 / r^2.
@end display
@end ifinfo
@ifnotinfo
@displaymath
  F = k_{\rm C} { {q_1 q_2} \over {r^2} }.
@end displaymath
@end ifnotinfo
@c end noman
@c
@c man .EQ
@c man delim $$
@c man .EN
@c man .if n \fIr\fP:
@c man .if t $r$:
@c man .RS 5n
@c man .PP
@c man .if n \fIF\fP = \fIk\fP_C \fIq\fP_1\ \fIq\fP_2\ /\ \fIr\fP^2.
@c man .if t \{\
@c man .EQ
@c man F = k sub roman C { q sub 1 q sub 2} over r sup 2.
@c man .EN
@c man .\}
@c man .RE

@noindent
Ampere's law gives the electromagnetic force per unit length
between two current-carrying conductors separated by a distance
@c noman
@math{r}:
@ifinfo
@display

F/l = 2 k_A I_1 I_2 / r.
@end display
@end ifinfo
@ifnotinfo
@displaymath
  { F \over \ell } = 2 k_{\rm A} { {I_1 I_2} \over {r} } .
@end displaymath
@end ifnotinfo
@c end noman
@c
@c man .if n \fIr\fP:
@c man .if t $r$:
@c man .RS 5n
@c man .PP
@c man .if n \fIF\fP/\fIl\fP = 2 \fIk\fP_A \fII\fP_1\ \fII\fP_2\ /\ \fIr\fP.
@c man .if t \{\
@c man .EQ
@c man F over l = 2 k sub roman A { I sub 1 I sub 2 } over r .
@c man .EN
@c man .\}
@c man .RE

@noindent
The two constants,
@c noman
@ifnotinfo
@math{k_{\rm C}} and @math{k_{\rm A}},
@end ifnotinfo
@ifinfo
k_C and k_A,
@end ifinfo
are related by the square of the speed of light:
@ifinfo
k_A = k_C / c^2.
@end ifinfo
@ifnotinfo
@displaymath
k_{\rm A} = k_{\rm C} / c^{2}.
@end displaymath
@end ifnotinfo
@c end noman
@c
@c man .if n \fIk\fP_C and \fIk\fP_A,
@c man .if t $k sub roman C$ and $k sub roman A$,
@c man are related by the square of the speed of light:
@c man .if n \fIk\fP_A\ =\ \fIk\fP_C\ /\ \fIc\fP^2.
@c man .if t $k sub roman A = k sub roman C / c sup 2$.

In the SI, the constants have dimensions, and an additional base unit,
the ampere, measures electric current.  The CGS systems do not define
new base units, but express charge and current as derived units in
terms of mass, length, and time.  In the ESU system, the constant for
Coulomb's law is chosen to be unity and dimensionless, which defines
the unit of charge.  In the EMU system, the constant for Ampere's law
is chosen to be unity and dimensionless, which defines a unit of
current.  The Gaussian system usually uses the ESU units for charge
and current; it chooses another constant so that the units for the
electric and magnetic fields are the same.  The Heaviside--Lorentz
system is ``rationalized'' so that factors of
@c noman
@math{4\pi}
@c end noman
@c
@c man .if n 4{pi}
@c man .if t 4\(*p
do not appear in
Maxwell's equations.  The SI system is similarly rationalized, but the
other CGS systems are not.  In the Heaviside--Lorentz (HLU) system the
factor of
@c noman
@math{4\pi}
@c end noman
@c
@c man .if n 4{pi}
@c man .if t 4\(*p
appears in Coulomb's law instead; this system differs
from the Gaussian system by factors of
@c noman
@math{\sqrt{4\pi}}.
@c end noman
@c
@c man .if n the square root of 4{pi}
@c man .if t \(sr\o'\[sqrtex]4'\o'\[sqrtex]\(*p'\^.

The dimensions of electrical quantities in the various CGS systems are
different from the SI dimensions for the same units;
strictly, conversions between these systems and SI are not possible.
But units in different systems relate to the same physical quantities,
so there is a @emph{correspondence} between these units.
The @command{units} program defines the units so that you can convert
between corresponding units in the various systems.

@node Specifying CGS Units
@subsection Specifying CGS Units
@cindex CGS units, specifying

The CGS definitions involve
@c noman
@ifinfo
cm^(1/2) and g^(1/2)
@end ifinfo
@ifnotinfo
@math {{\rm cm}^{1/2}} and @math{{\rm g}^{1/2}},
@end ifnotinfo
@c end noman
@c
@c man .if n cm^(1/2) and g^(1/2),
@c man .if t cm$"" sup {1/2}$ and g$"" sup {1/2}$,
@c man
@c
which is problematic because @command{units} does not normally support
fractional roots of base units.  The @option{--units} (@option{-u})
option allows selection of a CGS unit system and works around this
restriction by introducing base units for the square roots of length
and mass: @samp{sqrt_cm} and @samp{sqrt_g}.  The centimeter then
becomes @samp{sqrt_cm^2} and the gram, @samp{sqrt_g^2}.  This allows
working from equations using the units in the CGS system, and
enforcing dimensional conformity within that system.  Recognized CGS
arguments to the @option{--units} option are @samp{gauss[ian]},
@samp{esu}, @samp{emu}, @samp{lhu}; the argument is case insensitive.
You can also give @samp{si} which just enforces the default SI mode
and displays @samp{(SI)} at the @w{@samp{You have:}} prompt to
emphasize the units mode.  Some other types of units are also
supported as described below.  Giving an unrecognized system generates
a warning, and @command{units} uses SI units.

The changes resulting from the @option{--units} option are actually
controlled by the @env{UNITS_SYSTEM} environment variable.  If you
frequently work with one of the supported CGS units systems, you may set
this environment variable rather than giving the @option{--units} option
at each invocation.  As usual, an option given on the command line
overrides the setting of the environment variable. For example, if you would
normally work with Gaussian units but might occasionally work with
SI, you could set @env{UNITS_SYSTEM} to @samp{gaussian} and specify
SI with the @option{--units} option.
Unlike the argument to the @option{--units} option, the value of
@env{UNITS_SYSTEM} @emph{is} case sensitive, so setting a value of
@samp{EMU} will have no effect other than to give an error message and
set SI units.

The CGS definitions appear as conditional settings in the standard
units data file, which you can consult for more information on how
these units are defined, or on how to define an alternate units system.

@node CGS Units Systems
@subsection CGS Units Systems
@cindex CGS Units Systems
@cindex units systems, CGS

The ESU system derives the electromagnetic units from its unit of
charge, the statcoulomb,
which is defined from
Coulomb's law.  The statcoulomb equals
@c noman
@ifinfo
@w{dyne^(1/2) cm} or @w{cm^(3/2) g^(1/2) s^(-1)}.
@end ifinfo
@c
@ifnotinfo
@math{{\rm dyne}^{1/2}\,{\rm cm}} or @math{{\rm cm}^{3/2}\,{\rm g}^{1/2}\,{\rm s}^{-1}}.
@end ifnotinfo
@c end noman
@c
@c man .if n dyne^(1/2)\ cm, or cm^(3/2)\ g^(1/2)\ s^(\(mi1).
@c man .if t $roman dyne sup {1/2} ^ roman cm$,
@c man .if t or $roman cm sup {3/2} ^ roman g sup {1/2} ^ roman s sup {-1}$.
The unit of current, the statampere, is @w{statcoulomb sec}, analogous to
the relationship in SI.  Other electrical units are then derived in a
manner similar to that for SI units; the units use the SI names prefixed
by @samp{stat-}, e.g., @samp{statvolt} or @samp{statV}.  The prefix
@samp{st-} is also recognized (e.g., @samp{stV}).

The EMU system derives the electromagnetic units from its unit of current,
the abampere, which is defined in terms of Ampere's law.  The abampere
is equal to
@c noman
@ifinfo
dyne^(1/2) or @w{cm^(1/2) g^(1/2) s^(-1)}.
@end ifinfo
@ifnotinfo
@math{{\rm dyne}^{1/2}} or
@math{{\rm cm}^{1/2}{\rm g}^{1/2}{\rm s}^{-1}}.
@end ifnotinfo
@c
@c end noman
@c
@c man .if n dyne^(1/2), or cm^(1/2)\ g^(1/2)\ s^(\(mi1).
@c man .if t $roman dyne sup {1/2}$,
@c man .if t or $roman cm sup {1/2} ^ roman g sup {1/2} ^ roman s sup{-1}$.
@c man .EQ
@c man delim off
@c man .EN
The unit of charge, the abcoulomb, is
@w{abampere sec}, again analogous to the SI relationship.
Other electrical units are then derived in a
manner similar to that for SI units; the units use the SI names prefixed
by @samp{ab-}, e.g., @samp{abvolt} or @samp{abV}.  The magnetic field
units include the gauss, the oersted and the maxwell.

The Gaussian units system, which was also known as the Symmetric
System,
uses the same charge and current units as the ESU system (e.g.,
@samp{statC}, @samp{statA}); it differs by defining the magnetic field
so that it has the same units as the electric field.  The resulting
magnetic field units are the same ones used in the EMU system: the
gauss, the oersted and the maxwell.

The Heaviside--Lorentz system appears to lack named units.  We define
five basic units, @samp{hlu_charge}, @samp{hlu_current}, @samp{hlu_volt}, @samp{hlu_efield} and
@samp{hlu_bfield} for conversions with this system.  It is important to
remember that with all of the CGS systems, the units may look the same
but mean something different.  The HLU system and Gaussian systems
both measure magnetic field using the same CGS dimensions, but the
amount of magnetic field with the same units is different in the two
systems.

@node Conversions Between Systems
@subsection Conversions Between Different Systems

The CGS systems define units that measure the same thing but may have
conflicting dimensions.  Furthermore, the dimensions of the
electromagnetic CGS units are never compatible with SI.
But if you measure charge in two different systems you have measured the
same physical thing, so there is a @emph{correspondence} between the
units in the different systems, and @command{units} supports conversions
between corresponding units.  When running with SI, @command{units}
defines all of the CGS units in terms of SI.  When you select a CGS
system, @command{units} defines the SI units and the other CGS system
units in terms of the system you have selected.

@example
@group
(Gaussian) You have: statA
           You want: abA
        * 3.335641e-11
        / 2.9979246e+10
(Gaussian) You have: abA
           You want: sqrt(dyne)
conformability error
        2.9979246e+10 sqrt_cm^3 sqrt_g / s^2
        1 sqrt_cm sqrt_g / s
@end group
@end example

@noindent
In the above example, @command{units} converts between the current
units statA and abA even though the abA, from the EMU system, has
incompatible dimensions.  This works because in Gaussian mode, the abA
is defined in terms of the statA, so it does not have the correct
definition for EMU; consequently, you cannot convert the abA to its EMU
definition.

One challenge of conversion is that because
the CGS system has fewer base units, quantities that have different
dimensions in SI may have the same dimension in a CGS system.  And
yet, they may not have the same conversion factor.  For example, the
unit for the @math{E} field and @math{B} fields are the same in the
Gaussian system, but the conversion factors to SI are quite
different.  This means that correct conversion is only possible if you
keep track of what quantity is being measured.  You cannot convert
statV/cm to SI without indicating which type of field the unit
measures.  To aid in dimensional analysis, @command{units} defines
various dimension units such as @samp{LENGTH}, @samp{TIME}, and @samp{CHARGE} to be the
appropriate dimension in SI.  The
electromagnetic dimensions such as @samp{B_FIELD} or @samp{E_FIELD} may be useful
aids both for conversion and dimensional analysis in CGS.  You
can convert them to or from CGS in order to perform SI conversions
that in some cases will not work directly due to dimensional incompatibilities.
This example shows how the Gaussian system uses the same units for all
of the fields, but they all have different conversion factors with
SI.

@example
@group
(Gaussian) You have: statV/cm
           You want: E_FIELD
        * 29979.246
        / 3.335641e-05
@end group
@group
(Gaussian) You have: statV/cm
           You want: B_FIELD
        * 0.0001
        / 10000
@end group
@group
(Gaussian) You have: statV/cm
           You want: H_FIELD
        * 79.577472
        / 0.012566371
@end group
@group
(Gaussian) You have: statV/cm
           You want: D_FIELD
        * 2.6544187e-07
        / 3767303.1
@end group
@end example

@noindent
The next example shows that the oersted cannot be converted directly
to the SI unit of magnetic field, A/m, because the dimensions
conflict.  We cannot redefine the ampere to make this work because
then it would not convert with the statampere.  But you can still do
this conversion as shown below.

@example
@group
(Gaussian) You have: oersted
           You want: A/m
conformability error
        1 sqrt_g / s sqrt_cm
        29979246 sqrt_cm sqrt_g / s^2
(Gaussian) You have: oersted
           You want: H_FIELD
        * 79.577472
        / 0.012566371
@end group
@end example


@node Natural Units
@c ---------------------------------------------------------------------
@section Natural Units
@c ---------------------------------------------------------------------
@cindex Natural units, using

Like the CGS units, ``natural'' units are an alternative to the SI
system used primarily physicists in different fields, with different
systems tailored to different fields of study.  These
systems are ``natural'' because the base measurements are defined
using physical constants instead of arbitrary values such as the meter
or second.  In different branches of physics, different physical constants
are more fundamental, which has given rise to a variety of incompatible natural
unit systems.

The supported systems are the ``natural'' units (which seem to have no
better name) used in high energy physics and cosmology, the Planck
units, often used by scientists working with gravity, and the Hartree
atomic units are favored by those working in physical chemistry and
condensed matter physics.

You can select the various natural units using the @option{--units}
option in the same way that you select the CGS units.  The ``natural''
units come in two types, a rationalized system derived from the
Heaviside--Lorentz units and an unrationalized system derived from the
Gaussian system.  You can select these using @samp{natural} and
@samp{natural-gauss} respectively.  For conversions in SI mode,
several unit names starting with @samp{natural} are available.
This ``natural'' system is defined by setting
@c noman
@math{\hbar},
@c end noman
@c
@c man .if n {hbar},
@c man .if t \[hbar],
@math{c} and the Boltzman
constant to 1.  Only a single base unit remains: the electron volt.

The Planck units exist in a variety of forms, and @command{units}
supports two.  Both supported forms are rationalized, in that factors
of
@c noman
@math{4\pi}
@c end noman
@c
@c man .if n 4{pi}
@c man .if t 4\(*p
do not appear in Maxwell's equations.  However, Planck units
can also differ based on how the gravitational constant is treated.
This system is similar to the natural units in that @math{c},
@c noman
@math{\hbar},
@c end noman
@c
@c man .if n {hbar},
@c man .if t \[hbar],
and
Boltzman's constant are set to 1, but in this system, Newton's
gravitational constant,
@c noman
@math{G},
@c end noman
@c
@c man \fIG\fP
is also fixed.  In the ``reduced'' Planck
system,
@c noman
@math{8 \pi G=1}
@c end noman
@c
@c man .EQ
@c man delim $$
@c man .EN
@c man .if n 8{pi}\fIG\fP\ =\ 1
@c man .if t $8 pi G = 1$
whereas in the unreduced system
@c noman
@math{G = 1}.
@c end noman
@c
@c man .if n \fIG\fP\ =\ 1.
@c man .if t $G = 1$.
The reduced system eliminates factors of
@c noman
@math{8 \pi}
@c end noman
@c
@c man .if n 8{pi}
@c man .if t 8\(*p
@c man .EQ
@c man delim off
@c man .EN
from the Einstein field equations for gravitation, so this is similar to
the process of forming rationalized units to simplify Maxwell's equations.
To obtain the unreduced system use the name @samp{planck} and for the
reduced Planck units, @samp{planck-red}.  Units such as
@samp{planckenergy} and @samp{planckenergy_red} enable you to convert
the unreduced and reduced Planck energy unit in SI mode between the
various systems.  In Planck units, all measurements are
dimensionless.

The final natural unit system is the Hartree atomic units.  Like the
Planck units, all measurements in the Hartree units are dimensionless,
but this system is defined by defined from completely different
physical constants: the electron mass, Planck's constant, the electron
charge, and the Coulomb constant are the defining physical
quantities, which are all set to unity.  To invoke this system with
the @option{--units} option use the name @samp{hartree}.


@node Prompt Prefix
@c ---------------------------------------------------------------------
@section Prompt Prefix
@c ---------------------------------------------------------------------
@cindex prompt prefix with CGS units
@cindex CGS units, prompt prefix

If a unit system is specified with the @option{--units} option, the
selected system's name is prepended to the @w{@samp{You have:}} prompt
as a reminder, e.g.,

@example
@group
(Gaussian) You have: stC
           You want:
        Definition: statcoulomb = sqrt(dyne) cm = 1 sqrt_cm^3 sqrt_g / s
@end group
@end example

@noindent
You can suppressed the prefix by including a line

@example
!prompt
@end example

@noindent
with no argument in a site or personal units data file.  The prompt can
be conditionally suppressed by including such a line within
@samp{!var} ... @samp{!endvar} constructs, e.g.,

@example
@group
!var UNITS_SYSTEM gaussian gauss
!prompt
!endvar
@end group
@end example

@noindent
This might be appropriate if you normally use Gaussian units and find
the prefix distracting but want to be reminded when you have selected a
different CGS system.

@node Logging Calculations
@c =====================================================================
@chapter Logging Calculations
@c =====================================================================
@cindex logging calculations
@cindex log file

The @option{--log} option allows you to save the results of calculations
in a file; this can be useful if you need a permanent record of your
work.  For example, the fluid-flow conversion in
@ref{Complicated Unit Expressions}, is lengthy, and if you were to use
it in designing a piping system, you might want a record of it for the
project file.  If the interactive session

@example
@group
# Conversion factor A1 for pressure drop
# dP = A1 rho f L Q^2/d^5
You have: (8/pi^2) (lbm/ft^3)ft(ft^3/s)^2(1/in^5) # Input units
You want: psi
        * 43.533969
        / 0.022970568
@end group
@end example

@noindent
were logged, the log file would contain

@example
@group
### Log started Fri Oct 02 15:55:35 2015

# Conversion factor A1 for pressure drop
# dP = A1 rho f L Q^2/d^5
From: (8/pi^2) (lbm/ft^3)ft(ft^3/s)^2(1/in^5)   # Input units
To:   psi
        * 43.533969
        / 0.022970568
@end group
@end example

@noindent
The time is written to the log file when the file is opened.

The use of comments can help clarify the meaning of calculations for
the log.
The log includes conformability errors between the units at the
@w{@samp{You have:}} and @w{@samp{You want:}} prompts, but not other
errors, including lack of conformability of items in sums or differences
or among items in a unit list.  For example, a conversion between zenith
angle and elevation angle could involve

@example
@group
You have: 90 deg - (5 deg + 22 min + 9 sec)
                                   ^
Invalid sum or difference of non-conformable units
You have: 90 deg - (5 deg + 22 arcmin + 9 arcsec)
You want: dms
        84 deg + 37 arcmin + 51 arcsec
You have: _
You want: deg
        * 84.630833
        / 0.011816024
You have:
@end group
@end example

@noindent
The log file would contain

@example
@group
From: 90 deg - (5 deg + 22 arcmin + 9 arcsec)
To:   deg;arcmin;arcsec
        84 deg + 37 arcmin + 51 arcsec
From: _
To:   deg
        * 84.630833
        / 0.011816024
@end group
@end example

@noindent
The initial entry error (forgetting that minutes have dimension of time,
and that arcminutes must be used for dimensions of angle) does not
appear in the output.  When converting to a unit list alias,
@command{units} expands the alias in the log file.

The @samp{From:} and @samp{To:} tags are written to the log file even if
the @option{--quiet} option is given.  If the log file exists when
@command{units} is invoked, the new results are appended to the log file.
The time is written to the log file each time the file is opened.
The @option{--log} option is ignored when @command{units} is used
non-interactively.

@node Invoking Units
@c =====================================================================
@chapter Invoking @command{units}
@c =====================================================================
@cindex invoking units
@cindex command-line options

You invoke @command{units} like this:

@example
units [@var{options}] [@var{from-unit} [@var{to-unit}]]
@end example

@noindent
If the @var{from-unit} and @var{to-unit} are omitted, the program
will use interactive prompts to determine which conversions to perform.
@xref{Interactive Use}.
If both @var{from-unit} and @var{to-unit} are given, @command{units} will
print the result of that single conversion and then exit.
If only @var{from-unit} appears on the command line, @command{units} will
display the definition of that unit and exit.
Units specified on the command line may need
to be quoted to protect them from shell interpretation and to group
them into two arguments.  Note also that the @option{--quiet} option
is enabled by default if you specify @var{from-unit} on the command line.
@xref{Command Line Use}.

The default behavior of @command{units} can be changed by various
options given on the command line.  In most cases, the options may be
given in either short form (a single @samp{-} followed by a single
character)
or long form (@option{--} followed by a word or hyphen-separated words).
Short-form options are cryptic but require
less typing; long-form options require more typing but are more
explanatory and may be more mnemonic.  With long-form options you need
only enter sufficient characters to uniquely identify the option to
the program.  For example, @option{--out@tie{}%f} works, but
@option{--o@tie{}%f} fails because @command{units} has other long options
beginning with @samp{o}.  However, @option{--q} works because
@option{--quiet} is the only long option beginning with @samp{q}.

Some options require
arguments to specify a value (e.g., @option{-d@tie{}12} or
@option{--digits@tie{}12}).  Short-form options that do not take
arguments may be concatenated (e.g., @option{-erS} is equivalent to
@option{-e@tie{}-r@tie{}-S}); the last option in such a list may be one
that takes an argument (e.g., @option{-ed@tie{}12}).  With short-form
options, the space between an option and its argument is optional (e.g.,
@option{-d12} is equivalent to @option{-d@tie{}12}).  Long-form options may
not be concatenated, and the space between a long-form option and its
argument is required.  Short-form and long-form options may be
intermixed on the command line.  Options may be given in any order, but
when incompatible options (e.g., @option{--output-format} and
@option{--exponential}) are given in combination, behavior is controlled
by the last option given.  For example, @option{-o%.12f@tie{}-e} gives
exponential format with the default eight significant digits).

Many options can be set interactively; this can be especially helpful
for Windows users who start @command{units} from a shortcut.
@xref{Setting Options Interactively} for more information.

The following options are available:

@table @env
@item -c
@itemx --check
@opindex -c @r{(option for} @command{units}@r{)}
@opindex --check @r{(option for} @command{units}@r{)}
Check that all units and prefixes defined in units data files reduce to
primitive units.  Display a list of all units that cannot be reduced and
a list of units with circular definitions.  Also display some other
diagnostics about suspicious definitions in the units data file.  Only
definitions active in the current locale are checked.  You should always
run @command{units} with this option after modifying a units data file.

Some errors may hide other errors, so you should run @command{units}
with this option again after correcting any errors, and keep doing so
until there are no errors.

@item --check-verbose
@itemx --verbose-check
@opindex --check-verbose @r{(option for} @command{units}@r{)}
@opindex --verbose-check @r{(option for} @command{units}@r{)}
Like the @option{--check} option, this option displays a list of units that
cannot be reduced.  But it also lists the units as they are checked.
Because the @option{--check} option now catches circular unit
definitions that previously caused @command{units} to hang, this option
is no longer necessary.  It is retained only for compatibility with
previous versions.

@item --list-units
@opindex --list-units @r{(option for} @command{units}@r{)}
This option displays a list of all units and exits.  With output
redirected to a file, it can produce a list of all units in the
database, which may comprise multiple @command{units} data files.  It
can also be useful if you aren't sure of the name of a unit or want to find
all units of a particular type and you want a more advanced search than
is available with the interactive @kbd{search} command.
@xref{Finding Units} for some examples of how this option can be used.

@item -d @var{ndigits}
@itemx --digits @var{ndigits}
@opindex -d @r{(option for} @command{units}@r{)}
@opindex --digits @r{(option for} @command{units}@r{)}
Set the number of significant digits in the output to the value
specified (which must be greater than zero).  For example,
@option{-d@tie{}12} sets the number of significant digits to 12.
With exponential output, @command{units} displays one digit to the left
of the decimal point and eleven digits to the right of the decimal point.
On most systems, the maximum number of internally meaningful digits is
15; if you specify a greater number than your system's maximum, @command{units}
will print a warning and set the number to the largest meaningful
value.  To directly set the maximum value, give an argument
of @code{max} (e.g., @option{-d@tie{}max}).  Be aware, of course, that
``significant'' here refers only to the @emph{display} of numbers; if
results depend on physical constants not known to this precision, the
physically meaningful precision may be less than that shown.  The
@option{--digits} option is incompatible with the @option{--output-format}
option; if you give them both, the format is controlled by the last
option given.

@item -e
@itemx --exponential
@opindex -e @r{(option for} @command{units}@r{)}
@opindex --exponential @r{(option for} @command{units}@r{)}
Set the numeric output format to exponential (i.e., scientific
notation), like that used in the Unix @command{units} program.
The default precision is eight significant digits (seven digits to the
right of the decimal point); this can be changed with the
@option{--digits} option.  The @option{--exponential}
option is incompatible with the @option{--output-format} option; if you
give them both, the format is controlled by the last option given.

@item -o @var{format}
@itemx --output-format @var{format}
@opindex -o @r{(option for} @command{units}@r{)}
@opindex --output-format @r{(option for} @command{units}@r{)}
This option affords complete control over the numeric output format
using the specified @var{format}. The format is a single floating
point numeric format for the @code{printf} function in the
C programming language.  All compilers support the format types @samp{g}
and @samp{G} to specify significant digits, @samp{e} and @samp{E} for
scientific notation, and @samp{f} for fixed-point decimal.
The ISO C99 standard introduced the @samp{F} type for fixed-point
decimal and the @samp{a} and @samp{A} types for hexadecimal
floating point; these types are allowed with compilers that support
them.  The default format is @samp{%.8g}; for greater precision, you
could specify @option{-o@tie{}%.15g}.  Unlike with the @option{--digits}
option, you can specify any desired precision, though not all digits may
be meaningful. @xref{Numeric Output Format}, and the documentation for
@code{printf} for more detailed descriptions of the format
specification.  The @option{--output-format} option affords the greatest
control of the output appearance, but requires at least rudimentary
knowledge of the @code{printf} format syntax.  If you don't want to
bother with the @code{printf} syntax, you can specify greater precision
more simply with the @option{--digits} option or select exponential
format with @option{--exponential}.  The @option{--output-format} option
is incompatible with the @option{--exponential} and @option{--digits}
options; if you give either in combination with @option{--output-format},
the format is controlled by the last option given.

@item -f @var{filename}
@itemx --file @var{filename}
@opindex -f @r{(option for} @command{units}@r{)}
@opindex --file @r{(option for} @command{units}@r{)}
Instruct @command{units} to load the units file @var{filename}.  You
can specify up to 25 units files on the command line.  When you use
this option, @command{units} will load @emph{only} the files you list
on the command line; it will not load the standard file or your
personal units file unless you explicitly list them.  If @var{filename}
is the empty string (@w{@option{-f ""}}), the default main units file (or
that specified by @env{UNITSFILE}) will be loaded in addition to any
others specified with @option{-f}.

@item -L @var{logfile}
@itemx --log @var{logfile}
@opindex -L @r{(option for} @command{units}@r{)}
@opindex --log @r{(option for} @command{units}@r{)}
Save the results of calculations in the file @var{logfile}; this can be
useful if it is important to have a record of unit conversions or other
calculations that are to be used extensively or in a critical activity
such as a program or design project.  If @var{logfile} exits, the new
results are appended to the file.
This option is ignored when @command{units} is used non-interactively.
@xref{Logging Calculations}, for a more detailed description and some
examples.

@item -H @var{filename}
@itemx --history @var{filename}
@opindex -H @r{(option for} @command{units}@r{)}
@opindex --history @r{(option for} @command{units}@r{)}
Instruct @command{units} to save history to @var{filename}, so that a
record of your commands is available for retrieval across different
@command{units} invocations.  To prevent the history from being saved
set @var{filename} to the empty string (@w{@option{-H ""}}).  This
option has no effect if readline is not available.

@item -h
@itemx --help
@opindex -h @r{(option for} @command{units}@r{)}
@opindex --help @r{(option for} @command{units}@r{)}
Print out a summary of the options for @command{units}.

@item -m
@itemx --minus
@opindex -m @r{(option for} @command{units}@r{)}
@opindex --minus @r{(option for} @command{units}@r{)}
Causes @samp{-} to be interpreted as a subtraction operator.  This is
the default behavior.

@item -p
@itemx --product
@opindex -p @r{(option for} @command{units}@r{)}
@opindex --product @r{(option for} @command{units}@r{)}
Causes @samp{-} to be interpreted as a multiplication operator when it
has two operands.  It will act as a negation operator when it has only one
operand: @samp{(-3)}.  By default @samp{-} is treated as a
subtraction operator.

@item --oldstar
@opindex --oldstar @r{(option for} @command{units}@r{)}
Causes @samp{*} to have the old-style precedence, higher than the
precedence of division so that @samp{1/2*3} will equal @samp{1/6}.

@item --newstar
@opindex --newstar @r{(option for} @command{units}@r{)}
Forces @samp{*} to have the new (default) precedence that follows
the usual rules of algebra: the precedence of @samp{*} is the same as
the precedence of @samp{/}, so that @samp{1/2*3} will equal @samp{3/2}.

@item -r
@itemx --round
When converting to a combination of units given by a unit list, round
the value of the last unit in the list to the nearest integer.

@item -S
@itemx --show-factor
When converting to a combination of units specified in a list,
always show a non-unity factor before a unit that
begins with a fraction with a unity denominator.  By default, if the
unit in a list begins with fraction of the form 1|@var{x} and
its multiplier is an integer other than 1, the fraction is given as the
product of the multiplier and the numerator (e.g., @samp{3|8@tie{}in}
rather than @samp{3 * 1|8@tie{}in}).  In some cases, this is not what is
wanted; for example, the results for a cooking recipe might show
@samp{3 * 1|2@tie{}cup} as @samp{3|2@tie{}cup}.
With the @option{--show-factor} option, a
result equivalent to 1.5 cups will display as @samp{3 * 1|2@tie{}cup}
rather than @samp{3|2@tie{}cup}.  A user-specified fractional unit with
a numerator other than 1 is never overridden, however---if a unit list
specifies @samp{3|4 cup;1|2 cup}, a result equivalent to 1@tie{}1/2 cups
will always be shown as @samp{2 * 3|4@tie{}cup} whether or not the
@option{--show-factor} option is given.

@item --conformable
@opindex --conformable @r{(option for} @command{units}@r{)}
In non-interactive mode, show all units conformable with the original
unit expression.  Only one unit expression is allowed; if you give more
than one, @command{units} will exit with an error message and return
failure.

@item -v
@itemx --verbose
@opindex -v @r{(option for} @command{units}@r{)}
@opindex --verbose @r{(option for} @command{units}@r{)}
Give slightly more verbose output when converting units.  When combined
with the @option{-c} option this gives the same effect as
@option{--check-verbose}.  When combined with @option{--version}
produces a more detailed output, equivalent to the @option{--info}
option.

@item -V
@itemx --version
@opindex -V @r{(option for} @command{units}@r{)}
@opindex --version @r{(option for} @command{units}@r{)}
Print the program version number, tell whether the @command{readline}
library has been included, tell whether UTF-8 support has been included;
give the locale, the location of the default main units data file, and
the location of the personal units data file; indicate if the personal
units data file does not exist.

When given in combination with the @option{--terse} option, the program
prints only the version number and exits.

When given in combination with the @option{--verbose} option, the
program, the @option{--version} option has the same effect as the
@option{--info} option below.

@item -I
@itemx --info
@opindex -I @r{(option for} @command{units}@r{)}
@opindex --info @r{(option for} @command{units}@r{)}
Print the information given with the @option{--version} option, show the
pathname of the units program, show the status of the @env{UNITSFILE}
and @env{MYUNITSFILE} environment variables, and additional information
about how @command{units} locates the related files.  On systems running
Microsoft Windows, the status of the @env{UNITSLOCALE} environment
variable and information about the related locale map are also given.
This option is usually of interest only to developers and
administrators, but it can sometimes be useful for troubleshooting.

Combining the @option{--version} and @option{--verbose} options has the
same effect as giving @option{--info}.

@item -U
@itemx --unitsfile
@opindex -U @r{(option for} @command{units}@r{)}
@opindex --unitsfile @r{(option for} @command{units}@r{)}
Print the location of the default main units data file and exit; if the
file cannot be found, print ``Units data file not found''.

@item -u @var{units-system}
@itemx --units @var{units-system}
@opindex -u @r{(option for} @command{units}@r{)}
@opindex --units @r{(option for} @command{units}@r{)}
Specify a CGS units system or natural units system.  The supported units
systems are: gauss[ian], esu, emu, hlu, natural, natural-gauss,
hartree, planck, planck-red, and si. @xref{Alternative Unit Systems},
for further information about these unit systems.

@item -l @var{locale}
@itemx --locale @var{locale}
@opindex --locale @r{(option for} @command{units}@r{)}
@opindex -l @r{(option for} @command{units}@r{)}
Force a specified locale such as @samp{en_GB} to get British definitions
by default.
This overrides the locale determined from system settings or environment
variables. @xref{Locale}, for a description of locale format.

@item -n
@itemx --nolists
Disable conversion to unit lists.

@item -s
@itemx --strict
@opindex -s @r{(option for} @command{units}@r{)}
@opindex --strict @r{(option for} @command{units}@r{)}
Suppress conversion of units to their reciprocal units.  For
example, @command{units} will normally convert hertz to seconds
because these units are reciprocals of each other.  The strict option
requires that units be strictly conformable to perform a conversion, and
will give an error if you attempt to convert hertz to seconds.

@item -1
@itemx --one-line
@opindex -1 @r{(option for} @command{units}@r{)}
@opindex --one-line @r{(option for} @command{units}@r{)}
Give only one line of output (the forward conversion); do not print
the reverse conversion.  If a reciprocal conversion is
performed, then @command{units} will still print the ``reciprocal
conversion'' line.

@item -t
@itemx --terse
@opindex -t @r{(option for} @command{units}@r{)}
@opindex --terse @r{(option for} @command{units}@r{)}
Print only a single conversion factor without any clutter, or if you
request a definition, prints just the definition (including its units).
This option can be used when calling @command{units} from another
program so that the output is easy to parse.
The command @code{units --terse mile m} produces the output @samp{1690.344}.
This option has the combined
effect of these options:  @option{--strict} @option{--quiet} @option{--one-line}
@option{--compact}.  When combined with @option{--version} it produces
a display showing only the program name and version number.





@item --compact
@opindex --compact @r{(option for} @command{units}@r{)}
Give compact output featuring only the conversion factor; the
multiplication and division signs are not shown, and there is no leading
whitespace.  If you convert to a unit list, then the output is a
semicolon separated list of factors.
This turns off the @option{--verbose} option.

@item -q
@itemx --quiet
@itemx --silent
@opindex -q @r{(option for} @command{units}@r{)}
@opindex --quiet @r{(option for} @command{units}@r{)}
@opindex --silent @r{(option for} @command{units}@r{)}
Suppress the display of statistics about the number of units loaded,
any messages printed by the units database,
and the prompting of the user for units.  This option does not
affect how @command{units} displays the results.  This option is
turned on by default if you invoke @command{units} with a unit
expression on the command line.

@end table

@node Setting Options Interactively
@c =====================================================================
@chapter Setting Options Interactively
@c =====================================================================
@cindex set
@cindex setting options interactively
@cindex options, setting interactively

Many command-line options can also be set interactively,
obviating the need to quit and restart @command{units} to change
the values.  This can be especially helpful for Windows users who
start @command{units} from a shortcut.

Typing @w{@kbd{set}} will display a list of all options that
can be set interactively, as well as the current and possible
values; options set to other than default values have an asterisk
(@samp{*}) prepended. For example,

@example
You have: set
  q[uiet] = no         (y|n) do/don't suppress prompting
  o[neline] = no       (y|n) do/don't suppress the second line of output
  st[rict] = no        (y|n) do/don't suppress reciprocal unit conversion
                             (e.g. Hz<->s)
  t[erse] = no         (y|n) do/don't give very terse output
  c[ompact] = no       (y|n) do/don't suppress printing tab, SETFLAG, and '/'
                             characters in results
  v[erbose] = 1        (0|1|2) amount of information shown
 *d[igits] = 9         number of significant digits in output
  e[xponential] = no   (y|n) do/don't use exponential ("scientific") notation
 *f[ormat] = %.9g      printf(3) format specification
  u[nitlists] = yes    (y|n) do/don't allow conversion to unit lists
  r[ound] = no         (y|n) do/don't round last element of unit list output
                             to an integer
  sh[owfactor] = no    (y|n) do/don't show non-unity factor before 1|x
                             in multi-unit output
@end example

@noindent
Characters within the square brackets are optional, so settings
can be changed by entering only one or two characters.

The syntax for setting options is @w{@kbd{set} @var{option}@kbd{ = }@var{value}};
the spaces around the @samp{=} sign are optional.

Some settings are Boolean, enabled by entering @kbd{yes} (or just
@kbd{y}) and disabled by entering @kbd{no} (or just @kbd{n}).  For
example,

@example
@group
You have: set quiet = y
  quiet = yes
@end group
@end example

@noindent
Other settings take an integer value; for example,

@example
@group
You have: set d=11
  digits = 11
  format = %.11g
@end group
@end example

@noindent
The @code{format} setting takes a string, the format specification for
the @code{printf} function in the C programming language; for example,

@example
@group
You have: set format = %.9g
  format = %.9g
@end group
@end example

@noindent
Typing @w{@kbd{set} @var{option}} will display the current value
of @var{option}, for example

@example
@group
You have: set u
  unitlists = yes
You have: set d
  digits = 8
  format = %.8g
@end group
@end example

@noindent
For the @code{digits} and @code{exponential} options, the value
of @code{format} is also shown.

@node Scripting with Units
@c =====================================================================
@chapter Scripting with @command{units}
@c =====================================================================
@cindex scripting with @command{units}

Despite its numerous options, @command{units} cannot cover every
conceivable unit-conversion task.
For example, suppose we have found some mysterious scale, but cannot
figure out the units in which it is reporting.  We reach into our
pocket, place a 3.75-gram coin on the scale, and observe the scale
reading @samp{0.120}.  How do we quickly determine the units?  Or we
might wonder if a unit has any ``synonyms,'' i.e., other units with the
same value.

The capabilities of @command{units} are easily extended with simple
scripting.  Both questions above involve conformable units; on a system
with Unix-like utilities, conversions to conformable units could be
shown accomplished with the following script:

@set codequoteundirected
@set codequotebacktick
@example
@group
#!/bin/sh

progname=`basename $0 .sh`
umsg="Usage: $progname [<number>] unit"

if [ $# -lt 1 ]
then
    echo "$progname: missing quantity to convert"
    echo "$umsg"
    exit 1
fi

for unit in `units --conformable "$*" | cut -f 1 -d ' '`
do
    echo "$*"   # have -- quantity to convert
    echo $unit  # want -- conformable unit
done | units --terse --verbose
@end group
@end example
@clear codequotebacktick
@clear codequoteundirected

@noindent
When @command{units} is invoked with no non-option arguments, it reads
@var{have}/@var{want} pairs, on alternating lines, from its standard
input, so the task can be accomplished with only two invocations of
@command{units}.  This avoids the computational overhead of needlessly
reprocessing the units database for each conformable unit, as well as
the inherent system overhead of process invocation.

By itself, the script is not very useful.  But it could be used in
combination with other commands to address specific tasks.  For example,
running the script through a simple output filter could help solve the
scale problem above.  If the script is named @command{conformable},
running

@example
$ conformable 3.75g | grep 0.120
@end example

@noindent
gives
@example
@group
        3.75g = 0.1205653 apounce
        3.75g = 0.1205653 fineounce
        3.75g = 0.1205653 ozt
        3.75g = 0.1205653 tradewukiyeh
        3.75g = 0.1205653 troyounce
@end group
@end example

@noindent
So we might conclude that the scale is calibrated in troy ounces.

We might run
@example
@group
$ units --verbose are
        Definition: 100 m^2 = 100 m^2
@end group
@end example

@noindent
and wonder if @samp{are} has any synonyms, value.  To find out, we could
run

@example
@group
$ conformable are | grep "= 1 "
        are = 1 a
        are = 1 are
@end group
@end example

@node Output Styles
@c =====================================================================
@chapter Output Styles
@c =====================================================================
The output can be tweaked in various ways using command line options.
With no options, the output looks like this

@example
@group
$ units
Currency exchange rates from FloatRates (USD base) on 2023-07-08
3612 units, 109 prefixes, 122 nonlinear units

You have: 23ft
You want: m
        * 7.0104
        / 0.14264521
You have: m
You want: ft;in
        3 ft + 3.3700787 in
@end group
@end example

@noindent
This is arguably a bit cryptic; the @option{--verbose}
option makes clear what the output means:

@example
@group
$ units --verbose
Currency exchange rates from FloatRates (USD base) on 2023-07-08
3612 units, 109 prefixes, 122 nonlinear units

You have: 23 ft
You want: m
        23 ft = 7.0104 m
        23 ft = (1 / 0.14264521) m
You have: meter
You want: ft;in
        meter = 3 ft + 3.3700787 in
@end group
@end example

@noindent
The @option{--quiet} option suppresses the clutter displayed when
@command{units} starts, as well as the prompts to the user.
This option is enabled by default when you
give units on the command line.

@example
@group
$ units --quiet
23 ft
m
        * 7.0104
        / 0.14264521

$ units 23ft m
        * 7.0104
        / 0.14264521
@end group
@end example

@noindent
The remaining style options allow you to display only numerical values
without the tab or the multiplication and division signs, or to display just a
single line showing the forward conversion:

@set codequoteundirected
@example
@group
$ units --compact 23ft m
7.0104
0.14264521

$ units --compact m 'ft;in'
3;3.3700787

$ units --one-line 23ft m
        * 7.0104

$ units --one-line 23ft 1/m
        reciprocal conversion
        * 0.14264521

$ units --one-line 23ft kg
conformability error
        7.0104 m
        1 kg
@end group
@end example

@noindent
Note that when converting to a unit list, the @option{--compact}
option displays a semicolon separated list of results.  Also be aware
that the
@option{one-line} option doesn't live up to its name if you
execute a reciprocal conversion or if you get a conformability error.
The former case can be prevented using the @option{--strict} option,
which suppresses reciprocal conversions.
Similarly you can suppress unit list conversion using
@option{--nolists}.
It is impossible to prevent
the three line error output.

@example
@group
$ units --compact --nolists m 'ft;in'
Error in 'ft;in': Parse error

$ units --one-line --strict 23ft 1/m
@end group
@end example

@noindent
The various style options can be combined appropriately.  The ultimate
combination is the @option{--terse} option, which combines
@option{--strict}, @option{--quiet}, @option{--one-line},
and @option{--compact} to produce the minimal output,
just a single number for regular conversions and a semicolon
separated list for conversion to unit lists.  This will likely be the
best choice for programs that want to call @command{units} and then
process its result.

@example
@group
$ units --terse 23ft m
7.0104

$ units --terse m 'ft;in'
3;3.3700787

$ units --terse 23ft 1/m
conformability error
7.0104 m
1 / m

$ units --terse '1 mile'
1609.344 m

$ units --terse mile
5280 ft = 1609.344 m
@end group
@end example
@clear codequoteundirected


@node Defining Your Own Units
@c =====================================================================
@chapter Adding Your Own Definitions
@c =====================================================================

@menu
* Units Data Files::                Where are units defined?
* Defining New Units::              Writing your own unit and prefix definitions
* Defining Nonlinear Units::        Writing your own nonlinear unit definitions
* Piecewise Linear Units::          Writing your own piecewise linear definitions
* Defining Multivariate Functions:: Writing your own multivariate function definitions
* Defining Unit List Aliases::      Writing your own unit list aliases
@end menu

@node Units Data Files
@c ---------------------------------------------------------------------
@section Units Data Files
@c ---------------------------------------------------------------------
@cindex additional units data files
@cindex data files, additional
@cindex units data files, additional
@cindex @samp{!include}
@cindex command, @samp{!include}
@cindex including additional units data files

The units and prefixes that @command{units} can convert are defined in
the units data file, typically @file{/usr/share/units/definitions.units}.
If you can't find this file, run @w{@code{units --version}} to get
information on the file locations for your installation.
Although you can extend or modify this data file if you have appropriate
user privileges, it's usually better to put extensions in separate files
so that the definitions will be preserved if you update @command{units}.

You can include additional data files in the units database using
the @samp{!include} command in the standard units data file. For
example

@example
!include    /usr/local/share/units/local.units
@end example

@noindent
might be appropriate for a site-wide supplemental data file.
The location of the @samp{!include} statement in the standard units
data file is important; later definitions replace earlier ones,
so any definitions in an included file will override definitions before
the @samp{!include} statement in the standard units data file.
With normal invocation, no warning is given about redefinitions; to
ensure that you don't have an unintended redefinition, run
@w{@code{units -c}} after making changes to any units data file.

@cindex personal units data file
@cindex units data file, personal

If you want to add your own units in addition to or in place of
standard or site-wide supplemental units data files, you can include
them in the @file{.units} file in your home directory.  If this
file exists it is read after the standard units data file, so that any
definitions in this file will replace definitions of the same units in
the standard data file or in files included from the standard data
file.  This file will not be read if any units files are specified on
the command line.  (Under Windows the personal units file is
named @file{unitdef.units}.)  Running @w{@code{units -V}} will
display the location and name of your personal units file.

The @command{units} program first tries to determine your home
directory from the @env{HOME} environment variable.  On systems running
Microsoft Windows, if @env{HOME} does not exist, @command{units}
attempts to find your home directory from @env{HOMEDRIVE},
@env{HOMEPATH} and @env{USERPROFILE}.
@cindex MYUNITSFILE environment variable
@cindex environment variable, MYUNITSFILE
You can specify an arbitrary file as your personal units data file with
the @env{MYUNITSFILE} environment variable; if this variable exists, its
value is used without searching your home directory.
The default units data files are described in more detail in
@ref{Data Files}.

@node Defining New Units
@c ---------------------------------------------------------------------
@section Defining New Units and Prefixes
@c ---------------------------------------------------------------------
@cindex defining units
@cindex units, definition of
@cindex units definitions, adding
@cindex units definitions, changing
@cindex prefixes, definition of
@cindex defining prefixes
@cindex primitive units
@cindex units, primitive
@cindex @samp{!} to indicate primitive units
@cindex command, @samp{!} to indicate primitive units

A unit is specified on a single line by giving its name and an
equivalence.  Comments start with a @samp{#} character, which can appear
anywhere in a line.  The backslash character (@samp{\})
acts as a continuation
character if it appears as the last character on a line, making it
possible to spread definitions out over several lines if desired.
A file can be included by giving the command @samp{!include} followed by
the file's name.  The @samp{!} must be the first character on the
line.  The file will be sought in the same directory as the
parent file unless you give a full path.  The name of the file to be
included cannot contain spaces or the comment character @samp{#}.
@cindex include files

Unit names cannot begin or end with an underscore (@samp{_}) or a
decimal point (@samp{.}), and cannot contain any of the operator
characters @samp{+}, @samp{-}, @samp{*}, @samp{/}, @samp{|}, @samp{^},
@samp{;}, @samp{~}, a comma (@samp{,}), the comment character @samp{#},
or parentheses.
To facilitate copying and pasting from documents, several typographical
characters are converted to operators:
the figure
dash (U+2012), minus (@samp{@minus{}}; U+2212), and en
dash (`--'; U+2013) are converted to the operator @samp{-};
the multiplication sign (@samp{@U{00D7}}; U+00D7),
N-ary times operator (U+2A09),
dot operator (@samp{@U{22C5}}; U+22C5),
and middle dot (@samp{@U{00B7}}; U+00B7)
are converted to the operator @samp{*};
the division sign (@samp{@U{00F7}}; U+00F7)
is converted to the operator @samp{/};
and the fraction slash (U+2044) is converted to the operator @samp{|};
accordingly, none of these characters can appear in unit names.

Names cannot begin with a digit, and if a name ends in a digit other
than zero or one, then the name must end with an underscore followed
by a string consisting only of digits and decimal points.    For example, @samp{foo_2}, @samp{foo_3.14}, and
@samp{foo_3...9} are valid names but @samp{foo2} or @samp{foo_a2} are
invalid.  The underscore is necessary because without it,
@command{units} cannot determine whether @samp{foo2} is a unit name or
represents @samp{foo^2}.  Zero and one are exceptions because
@command{units} never interprets them as exponents.

You could define nitrous oxide as

@example
N2O     nitrogen 2  + oxygen
@end example

@noindent
but would need to define nitrogen dioxide as

@example
NO_2    nitrogen + oxygen 2
@end example

@noindent
Be careful to define new units in terms of old ones so that a
reduction leads to the primitive units, which are marked with @samp{!}
characters.  Dimensionless units are indicated by using the string
@samp{!dimensionless} for the unit definition.
@cindex dimensionless units, defining

When adding new units, be sure to use the @option{-c} option to check
that the new units reduce properly and that there are no circular
definitions that lead to endless loops.  Because some errors may hide
other errors, you should run @command{units} with the @option{-c} option
again after correcting any errors, and keep doing so until no errors are
displayed.

@cindex parentheses

If you define any units that contain
@samp{+} characters in their definitions,
carefully check them because the @option{-c} option
will not catch non-conformable sums.  Be careful with the @samp{-}
operator as well.  When used as a binary operator, the @samp{-}
character can perform addition or multiplication
depending on the options used to invoke @command{units}.
To ensure consistent behavior use @samp{-} only as a unary negation
operator when writing units definitions.  To multiply two units leave a
space or use the @samp{*} operator with care, recalling that it has
two possible precedence values and may require parentheses to ensure
consistent behavior.  To compute the difference
of @samp{foo} and @samp{bar} write @samp{foo+(-bar)} or even @samp{foo+-bar}.

You may wish to intentionally redefine a unit.  When you do this, and
use the @option{-c} option, @command{units} displays a warning message
about the redefinition.  You can suppress these warnings by redefining
a unit using a @samp{+} at the beginning of the unit name.  Do not
include any white space between the @samp{+} and the redefined unit
name.

Here is an example of a short data file that defines some basic
units:

@example
@group
m       !               # The meter is a primitive unit
sec     !               # The second is a primitive unit
rad     !dimensionless  # A dimensionless primitive unit
micro-  1e-6            # Define a prefix
minute  60 sec          # A minute is 60 seconds
hour    60 min          # An hour is 60 minutes
inch    72 m            # Inch defined incorrectly terms of meters
ft      12 inches       # The foot defined in terms of inches
mile    5280 ft         # And the mile
+inch   0.0254 m        # Correct redefinition, warning suppressed
@end group
@end example

@cindex parentheses
@noindent
A unit that ends with a @samp{-} character is a prefix.  If a prefix
definition contains any @samp{/} characters, be sure they are protected
by parentheses.  If you define @samp{half- 1/2}, then @samp{halfmeter}
would be equivalent to @samp{1 / (2@tie{}meter)}.

@node Defining Nonlinear Units
@c ---------------------------------------------------------------------
@section Defining Nonlinear Units
@c ---------------------------------------------------------------------
@cindex defining nonlinear units
@cindex nonlinear units, defining
@cindex nonlinear unit conversions
Some unit conversions of interest are nonlinear; for
example, temperature conversions between the Fahrenheit and Celsius
scales cannot be done by simply multiplying by conversion factors.

When you give a linear unit definition such as @samp{inch 2.54@tie{}cm}
you are providing information that @command{units} uses to convert
values in inches into primitive units of meters.  For nonlinear units,
you give a functional definition that provides the same information.

Nonlinear units are represented using a functional notation.
It is best to regard this notation not as a function call but
as a way of adding units to a number, much the same way that
writing a linear unit name after a number adds units to that number.
Internally, nonlinear units are defined by a pair of functions
that convert to and from linear units in the database, so that
an eventual conversion to primitive units is possible.

Here is an example nonlinear unit definition:

@example
@group
tempF(x) units=[1;K] domain=[-459.67,) range=[0,) \
            (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32
@end group
@end example

@noindent
A nonlinear unit definition comprises a unit name, a formal parameter
name, two functions, and optional specifications for units, the domain,
and the range (the domain of the inverse function).  The functions tell
@command{units} how to convert to and from the new unit.  To produce
valid results, the arguments of these functions need to have the correct
dimensions and be within the domains for which the functions are
defined.

@cindex parentheses

The definition begins with the unit name followed immediately (with no
spaces) by a @samp{(} character.  In the parentheses is the name of the
formal parameter.  Next is an optional specification of the units
required by the functions in the definition.  In the example above,
the @samp{units=[1;K]} specification indicates that the
@samp{tempF} function requires an input argument conformable with
@samp{1} (i.e., the argument is dimensionless), and that the inverse
function requires an input argument conformable with @samp{K}.  For
normal nonlinear units definition, the forward function will always take
a dimensionless argument; in general, the inverse function will need
units that match the quantity measured by your nonlinear unit.
Specifying the units enables @command{units} to perform error checking
on function arguments, and also to assign units to domain and range
specifications, which are described later.

Next the function definitions appear.  In the example above, the
@samp{tempF} function is defined by

@example
@group
tempF(x) = (x+(-32)) degF + stdtemp
@end group
@end example

@noindent
This gives a rule for converting @samp{x} in the units @samp{tempF}
to linear units of absolute temperature, which makes it possible to
convert from tempF to other units.

To enable conversions to Fahrenheit, you must give a rule for the
inverse conversions.  The inverse will be @samp{x(tempF)} and its
definition appears after a @samp{;} character.  In our example, the
inverse is

@example
@group
x(tempF) = (tempF+(-stdtemp))/degF + 32
@end group
@end example

@noindent
This inverse definition takes an absolute temperature as its argument
and converts it to the Fahrenheit temperature.  The inverse can be
omitted by leaving out the @samp{;} character and the inverse
definition, but then conversions @emph{to} the unit will not be
possible.  If the inverse definition is omitted, the @option{--check}
option will display a warning.  It is up to you to calculate and enter
the correct inverse function to obtain proper conversions; the
@option{--check} option tests the inverse at one point and prints an
error if it is not valid there, but this is not a guarantee that your
inverse is correct.

With some definitions, the units may vary.  For example, the definition

@example
@group
square(x)       x^2
@end group
@end example

@noindent
can have any arbitrary units, and can also take dimensionless arguments.
In such a case, you should @emph{not} specify units.
If a definition takes a root of its arguments, the definition is valid
only for units that yield such a root.  For example,

@example
@group
squirt(x)       sqrt(x)
@end group
@end example

@noindent
is valid for a dimensionless argument, and for arguments with even
powers of units.

@cindex domain, nonlinear unit definitions
@cindex range, nonlinear unit definitions

Some definitions may not be valid for all real numbers.  In such cases,
@command{units} can handle errors better if you specify an appropriate
domain and range.  You specify the domain and range as shown below:

@example
@group
baume(d) units=[1;g/cm^3] domain=[0,130.5] range=[1,10] \
         (145/(145-d)) g/cm^3 ; (baume+-g/cm^3) 145 / baume
@end group
@end example

@noindent
In this example the domain is specified after @samp{domain=} with
the two numerical endpoints given in brackets.  No spaces can appear before the @samp{=}.
In accord with mathematical
convention, square brackets indicate a closed interval (one that
includes its endpoints), and parentheses indicate an open interval (one
that does not include its endpoints).  An interval can be open or closed
on one or both ends; an interval that is unbounded on either end is
indicated by omitting the limit on that end.  For example, a quantity to
which decibel (dB) is applied may have any value greater than zero, so
the range is indicated by @samp{(0,)}:

@example
@group
decibel(x) units=[1;1] range=(0,) 10^(x/10); 10 log(decibel)
@end group
@end example

@noindent
If the domain or range is given, the second endpoint must be greater
than the first.  The intervals given for the domain and range must
be numbers and cannot include units or any calculations.  

The domain and range specifications can appear independently and in any
order along with the units specification.
The values for the domain and range endpoints are attached to the units
given in the units specification, and if necessary, the parameter value
is adjusted for comparison with the endpoints.  For example, if a
definition includes @samp{units=[1;ft]} and @samp{range=[3,)}, the range
will be taken as @w{3 ft} to infinity.  If the function is passed a
parameter of @w{@samp{900 mm}}, that value will be adjusted to
@w{2.9527559 ft}, which is outside the specified range.
If you omit the units specification from the previous example,
@command{units} can not tell whether you intend the lower endpoint
to be @w{3 ft} or @w{3 microfurlongs}, and can not adjust the
parameter value of @w{900 mm} for comparison.  Without units,
numerical values other than zero or plus or minus infinity for domain or
range endpoints are meaningless, and accordingly they are not allowed.  If
you give other values without units, then the definition will be ignored
and you will get an error message.

Although the units, domain, and range specifications are optional, it's
best to give them when they are applicable; doing so allows
@command{units} to perform better error checking and give more helpful
error messages.  Giving the domain and range also enables the
@option{--check} option to find a point in the domain to use for its
point check of your inverse definition.

You can make synonyms for nonlinear units by providing both the
forward and inverse functions; inverse functions can be obtained using
the @samp{~} operator.  So to create a synonym for @samp{tempF} you
could write

@example
@group
fahrenheit(x) units=[1;K] tempF(x); ~tempF(fahrenheit)
@end group
@end example

@noindent
This is useful for creating a nonlinear unit
definition that differs slightly from an existing definition without
having to repeat the original functions.  For example,

@example
dBW(x)     units=[1;W] range=[0,) dB(x) W ;  ~dB(dBW/W)
@end example

@noindent
If you wish a synonym to refer to an existing nonlinear unit without
modification, you can do so more simply by adding the synonym with
appended parentheses as a new unit, with the existing nonlinear
unit---without parentheses---as the definition.  So to create a synonym
for @samp{tempF} you could write

@example
fahrenheit()  tempF
@end example

@noindent
The definition must be a nonlinear unit; for example, the synonym

@example
fahrenheit()  meter
@end example

@noindent
will result in an error message when @command{units} starts.

@cindex units functions
@cindex functions of units
You may occasionally wish to define a function that operates on units.
This can be done using a nonlinear unit definition.  For example, the
definition below provides conversion between radius and the area of a
circle.  This definition requires a length as input and
produces an area as output, as indicated by the @samp{units=} specification.
Specifying the range as the nonnegative numbers can prevent cryptic
error messages.

@example
@group
circlearea(r) units=[m;m^2] range=[0,)   pi r^2 ; sqrt(circlearea/pi)
@end group
@end example

@node Piecewise Linear Units
@c ---------------------------------------------------------------------
@section Defining Piecewise Linear Units
@c ---------------------------------------------------------------------
@cindex defining piecewise linear units
@cindex linear interpolation
@cindex units, piecewise linear
@cindex piecewise linear units
Sometimes you may be interested in a piecewise linear unit such as
many wire gauges.  Piecewise linear units can be defined by specifying
conversions to linear units on a list of points.
Conversion at other points will be done by linear interpolation.
A partial definition of zinc gauge is

@example
@group
zincgauge[in] 1 0.002, 10 0.02, 15 0.04, 19 0.06, 23 0.1
@end group
@end example

@noindent
In this example, @samp{zincgauge} is the name of the piecewise linear
unit.  The definition of such a unit is indicated by the
embedded @samp{[} character.  After the bracket, you should indicate the
units to be attached to the numbers in the table.
No spaces can appear before the
@samp{]} character, so a definition like @samp{foo[kg meters]} is
invalid; instead write @samp{foo[kg*meters]}.  The definition of the
unit consists of a list of pairs optionally separated by commas.
This list defines a function for converting from the piecewise linear
unit to linear units.  The
first item in each pair is the function argument; the second item is the
value of the function at that argument (in the units specified in brackets).
In this example,
we define @samp{zincgauge} at five points.  For example, we set
@samp{zincgauge(1)} equal to @w{@samp{0.002 in}}.  Definitions like this
may be  more readable  if written using  continuation characters as

@example
@group
zincgauge[in] \
     1 0.002  \
    10 0.02   \
    15 0.04   \
    19 0.06   \
    23 0.1
@end group
@end example

@noindent
With the preceding definition, the following conversion can be
performed:

@example
@group
You have: zincgauge(10)
You want: in
    * 0.02
    / 50
You have: .01 inch
You want: zincgauge
    5
@end group
@end example

@noindent
If you define a piecewise linear unit that is not strictly monotonic,
then the inverse will not be well defined.  If the inverse is requested
for such a unit, @command{units} will return the smallest inverse.

After adding nonlinear units definitions, you should normally run
@w{@samp{units --check}} to check for errors.  If the @samp{units}
keyword is not given, the @option{--check} option checks a nonlinear unit
definition using a dimensionless argument, and then checks using an
arbitrary combination of units, as well as the square and cube of that
combination; a warning is given if any of these tests fail.  For
example,

@set codequoteundirected
@example
@group
Warning: function 'squirt(x)' defined as 'sqrt(x)'
         failed for some test inputs:
         squirt(7(kg K)^1): Unit not a root
         squirt(7(kg K)^3): Unit not a root
@end group
@end example
@clear codequoteundirected

@noindent
Running @w{@samp{units --check}} will print a warning if a
non-monotonic piecewise linear unit is encountered.  For example, the
relationship between ANSI coated abrasive designation and mean particle
size is non-monotonic in the vicinity of 800 grit:

@example
@group
ansicoated[micron] \
     . . .
    600 10.55 \
    800 11.5 \
    1000 9.5 \
@end group
@end example

@noindent
Running @w{@samp{units --check}} would give the error message

@set codequoteundirected
@example
@group
Table 'ansicoated' lacks unique inverse around entry 800
@end group
@end example
@clear codequoteundirected

@noindent
Although the inverse is not well defined in this region, it's not really
an error.  Viewing such error messages can be tedious, and if there are
enough of them, they can distract from true errors.  Error checking for
nonlinear unit definitions can be suppressed by giving the
@samp{noerror} keyword; for the examples above, this could be done as

@example
@group
squirt(x) noerror domain=[0,) range=[0,) sqrt(x); squirt^2
ansicoated[micron] noerror \
     . . .
@end group
@end example

@noindent
Use the @samp{noerror} keyword with caution.  The safest approach after
adding a nonlinear unit definition is to run @w{@samp{units --check}}
and confirm that there are no actual errors before adding the
@samp{noerror} keyword.

@node Defining Multivariate Functions
@c ---------------------------------------------------------------------
@section Defining Multivariate Functions
@c ---------------------------------------------------------------------
@cindex defining multivariate functions
@cindex multivariate functions, defining 
@cindex functions, multivariate

Some common dimensional calculations such as wind chill or body mass
index have more than one parameter.  To support these calculations,
@code{units} allows multivariate functions as unit definitions.  Unlike
the nonlinear units described above, multivariate functions provide only
a forward evaluation and are not invertible:  it is impossible to
convert a wind chill output back to the temperature and wind speed that
generated it.

A multivariate function definition is similar to that for other
nonlinear units.  For example, you could define @samp{bmi} like this, starting
with the unit's name followed immediately without white space by
a comma-separated parameter list:

@example
@group
bmi(ht,wt) units=[m,kg] domain=(0,)(0,) (wt/kg)/(ht/m)^2
@end group
@end example

@noindent
This defines a new unit, @samp{bmi}, that has two parameters,
@samp{height}, and @samp{weight}.  You are allowed to use white space
in the parameter list.  
The optional @samp{units=} specification (with no space before the
@samp{=}) provides a comma-separated list in
square brackets of units that provide the dimensions of the parameters. 
(Since multivariate units require the use of
commas, you cannot use them to specify the units in the @samp{units=} specification.)
If you list fewer units than the number of parameters, the remaining
parameters will allow any unit.  For univariate nonlinear units, a semicolon
introduces the units of the inverse.  The semicolon is not permitted
in the @samp{units=} list for multivariate functions.

You specify the domain, if desired, using @samp{domain=}, followed
(without white space) by
the intervals defining the domain of each parameter, either juxtaposed
or separated by commas.  The above example requires that both arguments
be strictly positive.  As usual, use square brackets to indicate closed
intervals.  The rules for domain intervals are the same as those described above
for nonlinear units.  If you need to indicate an unconstrained input give the
interval @samp{(,)}.  The intervals in the domain specification must
use numerical values; you cannot use units or calculations in the domain.  

The final part of the definition is the expression that defines the
unit.  Since inverses are not well-defined for multivariate units, you
cannot provide an inverse.  Since you cannot provide an inverse, you
also cannot provide a range, so the @samp{range=} specification is
invalid for multivariate functions.  

If you need to specify that a particular unit is of arbitrary dimension
when units appearing after it in the parameter list are of specified
dimension, you can do this using the special dimension specification,
@samp{*}.  Here is a toy example:

@example
@group
func(a,b) units=[*,1] domain=(,),[-1,1] a asin(b)
@end group
@end example

@noindent
In this example the first argument is permitted to be of any
dimension, but the second argument must be dimensionless.  The
first argument has no domain bounds, but the second one must
lie in the domain of the arcsine function.  

@node Defining Unit List Aliases
@c ---------------------------------------------------------------------
@section Defining Unit List Aliases
@c ---------------------------------------------------------------------
@cindex defining unit list aliases
@cindex unit list aliases, defining
@cindex @samp{!unitlist}
@cindex command, @samp{!unitlist}

Unit list aliases are treated differently from unit definitions,
because they are a data entry shorthand rather than a true definition
for a new unit.
A unit list alias definition begins with @samp{!unitlist} and includes the
alias and the definition;  for example, the aliases included in the
standard units data file are

@example
@group
!unitlist   hms     hr;min;sec
!unitlist   time    year;day;hr;min;sec
!unitlist   dms     deg;arcmin;arcsec
!unitlist   ftin    ft;in;1|8 in
!unitlist   usvol   cup;3|4 cup;2|3 cup;1|2 cup;1|3 cup;1|4 cup;\
                    tbsp;tsp;1|2 tsp;1|4 tsp;1|8 tsp
@end group
@end example

@noindent
Unit list aliases are only for unit lists, so the definition must
include a @samp{;}.  Unit list aliases can never be combined with
units or other unit list aliases, so the definition of @samp{time}
shown above could @emph{not} have been shortened to
@samp{year;day;hms}.

As usual, be sure to run @w{@samp{units --check}} to ensure that the
units listed in unit list aliases are conformable.

@node Numeric Output Format
@c =====================================================================
@chapter Numeric Output Format
@c =====================================================================
@cindex numeric output format
@cindex output format

@menu
* Format Specification::           The output format specification
* Flags::                          Optional format flags
* Field Width::                    Specifying output field width
* Precision::                      Specifying output precision
@end menu

By default, @code{units} shows results to eight significant digits in
general number format.  You can change this with the
@option{--exponential}, @option{--digits}, and @option{--output-format}
options.  The first sets an exponential format (i.e., scientific
notation) like that used in the original Unix @command{units} program,
the second allows you to specify a different number of significant
digits, and the last allows you to control the output appearance using
the format for the @code{printf} function in the C programming language.
If you only want to change the number of significant digits or specify
exponential format type, use the @option{--digits} and
@option{--exponential} options.  The @option{--output-format} option
affords the greatest control of the output appearance, but requires at
least rudimentary knowledge of the @code{printf} format syntax.
@xref{Invoking Units}, for descriptions of these options.

@node Format Specification
@c ---------------------------------------------------------------------
@section Format Specification
@c ---------------------------------------------------------------------
@cindex output format specification
@cindex format specification, output

The format specification recognized with the @option{--output-format}
option is a subset of that for @code{printf}.  The format specification has
the form
@c noman
@code{%}[@i{flags}][@i{width}][@code{.}@i{precision}]@i{type};
@c end noman
@c ifman
@ignore
.\".CW "%\fR[\fP\fIflags\fP\fR][\fP\fIwidth\fP\fR][\fP.\fIprecision\fP\fR]\fP\fItype\fP" ;
@code{%}[@i{flags}][@i{width}][\c
@code{.}@i{precision}]@i{type};
@end ignore
@c end ifman
it must begin with @samp{%}, and must end with a floating-point type
specifier:
@samp{g} or @samp{G} to specify the number of significant digits,
@samp{e} or @samp{E} for scientific notation, and @samp{f} for
fixed-point decimal.  The ISO C99 standard added the @samp{F} type for
fixed-point decimal and the @samp{a} and @samp{A} types for hexadecimal
floating point; these types are allowed with compilers that support
them.  Type length modifiers (e.g., @samp{L} to indicate a long double)
are inapplicable and are not allowed.

The default format for @command{units} is @samp{%.8g};
for greater precision, you could specify @option{-o@tie{}%.15g}.
The @samp{g} and @samp{G} format types use exponential format whenever
the exponent would be less than @math{-4}, so the value 0.000013
displays as @samp{1.3e-005}.  These types also use exponential notation
when the exponent is greater than or equal to the precision, so with the
default format, the value
@c
@c noman
@ifnotinfo
@math{5\times 10^7}
@end ifnotinfo
@ifinfo
5e7
@end ifinfo
@c end noman
@c man .if t .ig ++
@c man 5 \(mu 10^7
@c man .++
@c man .if n .ig ++
@c man .EQ
@c man 5 times 10 sup 7
@c man .EN
@c man .++
displays as @samp{50000000} and the value
@c
@c noman
@ifnotinfo
@math{5\times 10^8}
@end ifnotinfo
@ifinfo
5e8
@end ifinfo
@c end noman
@c man .if t .ig ++
@c man 5 \(mu 10^8
@c man .++
@c man .if n .ig ++
@c man .EQ
@c man 5 times 10 sup 8
@c man .EN
@c man .++
@c
displays as @samp{5e+008}.  If you prefer fixed-point display, you might
specify @option{-o@tie{}%.8f}; however, small numbers will display very
few significant digits, and values less than
@c
@c noman
@ifnotinfo
@math{5\times 10^{-8}}
@end ifnotinfo
@ifinfo
5e8
@end ifinfo
@c end noman
@c man .if t .ig ++
@c man 5 \(mu 10^\-8
@c man .++
@c man .if n .ig ++
@c man .EQ
@c man 5 times 10 sup -8
@c man .EN
@c man .++
@c
will show nothing but zeros.

The format specification may include one or more optional flags:
@samp{+}, @samp{@tie{}} (space), @samp{#}, @samp{-}, or @samp{0} (the
digit zero).  The digit-grouping flag
@c noman
@set codequoteundirected
@samp{'} (apostrophe)
@clear codequoteundirected
@c end noman
@c if the troff formatter is groff, ensure an ASCII single quote
@c man .ie \n(.g \(oq\(aq'
@c man .el \&'
is allowed with compilers that support it.  Flags are followed by an
optional value for the minimum field width, and an optional precision
specification that begins with a period (e.g., @samp{.6}).  The field
width includes the digits, decimal point, the exponent, thousands
separators (with the digit-grouping flag), and the sign if any of these
are shown.

@node Flags
@c ---------------------------------------------------------------------
@section Flags
@c ---------------------------------------------------------------------
@cindex output format flags
@cindex flags, output format

The @samp{+} flag causes the output to have a sign (@samp{+} or @samp{-}).
The space flag @samp{@tie{}} is similar to the @samp{+} flag, except
that when the value is positive, it is prefixed with a space rather than
a plus sign; this flag is ignored if the @samp{+} flag is also given.
The @samp{+} or @samp{@tie{}} flag could be useful if conversions might
include positive and negative results, and you wanted to align
the decimal points in exponential notation.
@c
The @samp{#} flag causes the output value to contain a decimal point in
all cases; by default, the output contains a decimal point only if there
are digits (which can be trailing zeros) to the right of the point.
With the @samp{g} or @samp{G} types, the @samp{#} flag also prevents the
suppression of trailing zeros.
@c
The digit-grouping flag
@c noman
@set codequoteundirected
@samp{'}
@clear codequoteundirected
@c end noman
@c if the troff formatter is groff, ensure an ASCII single quote
@c man .ie \n(.g \(oq\(aq'
@c man .el \&`''
shows a thousands separator in digits to the left of the decimal point.
@c (e.g., @samp{1,234.56}).
This can be useful when displaying large numbers in fixed-point decimal;
for example, with the format @samp{%f},

@example
You have: mile
You want: microfurlong
        * 8000000.000000
        / 0.000000
@end example

@noindent
the magnitude of the first result may not be immediately obvious without
counting the digits to the left of the decimal point.  If the thousands
separator is the comma (@samp{,}), the output with the format
@c noman
@set codequoteundirected
@samp{%'f}
@clear codequoteundirected
@c end noman
@c if the troff formatter is groff, ensure an ASCII single quote
@c man .ie \n(.g \(oq%\(aqf'
@c man .el `%'f'
might be

@example
You have: mile
You want: microfurlong
        * 8,000,000.000000
        / 0.000000
@end example

@noindent
making the magnitude readily apparent.  Unfortunately, few compilers
support the digit-grouping flag.

@c
With the @samp{-} flag, the output value is left aligned within the
specified field width.  If a field width greater than needed to show the
output value is specified, the @samp{0} (zero) flag causes the output
value to be left padded with zeros until the specified field width is
reached; for example, with the format @samp{%011.6f},

@example
You have: troypound
You want: grain
        * 5760.000000
        / 0000.000174
@end example

@noindent
The @samp{0} flag has no effect if the @samp{-} (left align) flag is
given.

@node Field Width
@c ---------------------------------------------------------------------
@section Field Width
@c ---------------------------------------------------------------------
@cindex output field width

By default, the output value is left aligned and shown with the minimum
width necessary for the specified (or default) precision.  If a field
width greater than this is specified, the value shown is right aligned,
and padded on the left with enough spaces to provide the specified field
width.  A width specification is typically used with fixed-point decimal
to have columns of numbers align at the decimal point; this arguably is
less useful with @command{units} than with long columnar output, but it
may nonetheless assist in quickly assessing the relative magnitudes of
results.  For example, with the format @samp{%12.6f},

@example
@group
You have: km
You want: in
        * 39370.078740
        /     0.000025
@end group
@group
You have: km
You want: rod
        *   198.838782
        /     0.005029
@end group
@group
You have: km
You want: furlong
        *     4.970970
        /     0.201168
@end group
@end example

@node Precision
@c ---------------------------------------------------------------------
@section Precision
@c ---------------------------------------------------------------------
@cindex output precision
@cindex precision, output

The meaning of ``precision'' depends on the format type.  With @samp{g}
or @samp{G}, it specifies the number of significant digits (like the
@option{--digits} option); with @samp{e}, @samp{E}, @samp{f}, or
@samp{F}, it specifies the maximum number of digits to be shown after
the decimal point.

@c
With the @samp{g} and @samp{G} format types, trailing zeros are
suppressed, so the results may sometimes have fewer digits than the
specified precision (as indicated above, the @samp{#} flag causes
trailing zeros to be displayed).

The default precision is 6, so @samp{%g} is equivalent to @samp{%.6g},
and would show the output to six significant digits.  Similarly,
@samp{%e} or @samp{%f} would show the output with six digits after the
decimal point.

The C @code{printf} function allows a precision of arbitrary size, whether or
not all of the digits are meaningful.  With most compilers, the maximum
internal precision with @command{units} is 15 decimal digits (or 13
hexadecimal digits).
With the @option{--digits} option, you are limited
to the maximum internal precision; with the @option{--output-format}
option, you may specify a precision greater than this, but it may not be
meaningful.  In some cases, specifying excess precision can result in
rounding artifacts.  For example, a pound is exactly 7000 grains, but
with the format @samp{%.18g}, the output might be

@example
You have: pound
You want: grain
        * 6999.9999999999991
        / 0.00014285714285714287
@end example

@noindent
With the format @samp{%.25g} you might get the following:

@example
You have: 1/3
You want:
        Definition: 0.333333333333333314829616256247
@end example

@noindent
In this case the displayed value includes a series of digits that represent the
underlying binary floating-point approximation to 1/3 but are not
meaningful for the desired computation.
In general, the result with excess precision is system dependent.
@c
The precision affects only the @emph{display} of numbers; if a result
relies on physical constants that are not known to the specified
precision, the number of physically meaningful digits may be less than
the number of digits shown.

See the documentation for @code{printf} for more detailed descriptions of the
format specification.

The @option{--output-format} option is incompatible with the
@option{--exponential} or @option{--digits} options; if the former is
given in combination with either of the latter, the format is controlled
by the last option given.

@node Localization
@c =====================================================================
@chapter Localization
@c =====================================================================
@cindex environment dependent definitions
@cindex localization
@cindex @samp{!locale}
@cindex command, @samp{!locale}
@cindex @samp{!endlocale}
@cindex command, @samp{!endlocale}
@cindex command, @samp{!endvar}
@cindex command, @samp{!var}
@cindex command, @samp{!varnot}
@cindex command, @samp{!set}
@cindex command, @samp{!message}

@menu
* Locale::                   What is a locale?
* Additional Localization::  When the locale isn't enough
@end menu

Some units have different values in different locations.  The
localization feature accommodates this by allowing a units data file to
specify definitions that depend on the user's locale.

@node Locale
@c ---------------------------------------------------------------------
@section Locale
@c ---------------------------------------------------------------------
@cindex locale
A locale is a subset of a user's environment that indicates the user's
language and country, and some attendant preferences, such as the
formatting of dates.  The @command{units} program attempts to determine
the locale from the POSIX @code{setlocale} function; if this cannot be done,
@command{units} examines the environment
variables @env{LC_CTYPE} and @env{LANG}.
On POSIX systems, a locale is of the form
@var{language}@code{_}@var{country}, where @var{language} is the
two-character code from ISO 639-1 and @var{country} is the two-character
code from ISO 3166-1; @var{language} is lower case and @var{country} is
upper case. For example, the POSIX locale for the United Kingdom is @code{en_GB}.

@cindex @file{locale_map.txt}
@cindex setlocale function
On systems running Microsoft Windows, the value returned by @code{setlocale}
is different from that on POSIX systems; @command{units} attempts to map
the Windows value to a POSIX value by means of a table in the file
@file{locale_map.txt} in the same directory as the other data files.  The
file includes entries for many combinations of language and country, and
can be extended to include other combinations.  The @file{locale_map.txt}
file comprises two tab-separated columns; each entry is of the form

@display
@var{Windows-locale}@ @ @ @var{POSIX-locale}
@end display

@noindent
where @var{POSIX-locale} is as described above, and @var{Windows-locale}
typically spells out both the language and country.  For example, the
entry for the United States is

@example
English_United States   en_US
@end example

@noindent
You can force @command{units} to run in a desired locale by using the
@option{-l} option.

In order to create unit definitions for a particular locale you begin
a block of definitions in a unit datafile with @samp{!locale} followed
by a locale name.  The @samp{!} must be the first character on the
line.  The @command{units} program reads the following
definitions only if the current locale matches.  You end the block of
localized units with @samp{!endlocale}.  Here is an example, which
defines the British gallon.

@example
@group
!locale en_GB
gallon       4.54609 liter
!endlocale
@end group
@end example

@node Additional Localization
@c ---------------------------------------------------------------------
@section Additional Localization
@c ---------------------------------------------------------------------

Sometimes the locale isn't sufficient to determine unit preferences.
There could be regional preferences, or a company could have specific
preferences.  Though probably uncommon, such differences could arise
with the choice of English customary units outside of English-speaking
countries.  To address this, @command{units} allows specifying
definitions that depend on environment variable settings.
The environment variables can be controlled based on the current locale,
or the user can set them to force a particular group of definitions.

A conditional block of definitions in a units data file begins with
either @samp{!var} or @samp{!varnot} following by an environment
variable name and then a space separated
list of values.  The leading @samp{!} must appear in the first column of a units
data file, and the conditional block is terminated by @samp{!endvar}.
Definitions in blocks beginning with @samp{!var} are executed only if the
environment variable is exactly equal to one of the listed values.
Definitions in blocks beginning with @samp{!varnot} are executed only if the
environment variable does @emph{not} equal any of the list values.

The inch has long been a customary measure of length in many places.
The word comes from the Latin @emph{uncia} meaning ``one twelfth,''
referring to its relationship with the foot.  By the 20th century, the
inch was officially defined in English-speaking countries relative to
the yard, but until 1959, the yard differed slightly among those
countries.  In France the customary inch, which was displaced in 1799
by the meter, had a different length based on a french foot.  These
customary definitions could be accommodated as follows:

@example
@group
!var INCH_UNIT usa
yard          3600|3937 m
!endvar
@end group
@group
!var INCH_UNIT canada
yard          0.9144 meter
!endvar
@end group
@group
!var INCH_UNIT uk
yard          0.91439841 meter
!endvar
@end group
@group
!var INCH_UNIT canada uk usa
foot          1|3 yard
inch          1|12 foot
!endvar
@end group
@group
!var INCH_UNIT france
foot          144|443.296 m
inch          1|12 foot
line          1|12 inch
!endvar
@end group
@group
!varnot INCH_UNIT usa uk france canada
!message Unknown value for INCH_UNIT
!endvar
@end group
@end example

@noindent
When @command{units} reads the above definitions it will check the
environment variable @env{INCH_UNIT} and load only the definitions for
the appropriate section.  If @env{INCH_UNIT} is unset or is not set to
one of the four values listed, then @command{units} will run the last
block.  In this case that block uses the
@samp{!message} command to display a warning message.  Alternatively
that block could set default values.

In order to create default values that are overridden by user settings
the data file can use the @samp{!set} command, which sets an
environment variable @emph{only if it is not already set};  these
settings are only for the current @command{units} invocation and do
not persist.  So if the example above were preceded by
@samp{!set INCH_UNIT france}, then this would make @samp{france} the
default value for @env{INCH_UNIT}.  If the user had set the variable
in the environment before invoking @command{units}, then
@command{units} would use the user's value.

To link these settings to the user's locale you combine the @samp{!set}
command with the @samp{!locale} command.
If you wanted to combine the above example with suitable locales you
could do by @emph{preceding} the above definition with the following:

@example
@group
!locale en_US
!set INCH_UNIT usa
!endlocale
!locale en_GB
!set INCH_UNIT uk
!endlocale
!locale en_CA
!set INCH_UNIT canada
!endlocale
!locale fr_FR
!set INCH_UNIT france
!endlocale
!set INCH_UNIT france
@end group
@end example

@noindent
These definitions set the overall default for @env{INCH_UNIT} to
@samp{france} and set default values for four locales appropriately.
The overall default setting comes last so that it only applies when
@env{INCH_UNIT} was not set by one of the other commands or by the
user.

If the variable given after @samp{!var} or @samp{!varnot} is undefined,
then @command{units} prints an error message and ignores the
definitions that follow.  Use @samp{!set} to create defaults to
prevent this situation from arising.  The @option{-c}
option only checks the definitions that are active for the current
environment and locale, so when adding new definitions take care to
check that all cases give rise to a well defined set of definitions.

@node Environment Vars
@c =====================================================================
@chapter Environment Variables
@c =====================================================================
@cindex environment variables

The @command{units} program uses the following environment variables:

@table @env
@item HOME
@cindex HOME environment variable
@cindex environment variable, HOME
Specifies the location of your home directory; it is used by
@command{units} to find a personal units data file @samp{.units}.  On
systems running Microsoft Windows, the file is @samp{unitdef.units}, and
if @env{HOME} does not exist, @command{units} tries to determine your
home directory from the @env{HOMEDRIVE} and @env{HOMEPATH} environment
variables; if these variables do not exist, units finally tries
@env{USERPROFILE}---typically @file{C:\Users\@var{username}} (Windows
Vista and Windows@tie{}7) or
@w{@file{C:\Documents and Settings\@var{username}}} (Windows@tie{}XP).

@item LC_CTYPE, LANG
@cindex LANG environment variable
@cindex LC_CTYPE environment variable
@cindex environment variable, LANG
@cindex environment variable, LC_CTYPE
Checked to determine the locale if @command{units} cannot obtain it
from the operating system.  Sections of the default main units data file
are specific to certain locales.

@item MYUNITSFILE
@cindex MYUNITSFILE environment variable
@cindex environment variable, MYUNITSFILE
Specifies your personal units data file.  If this variable exists,
@command{units} uses its value rather than searching your home
directory for @samp{.units}.  The personal units file will not be
loaded if any data files are given using the @option{-f} option.

@item PAGER
@cindex PAGER environment variable
@cindex environment variable, PAGER
@cindex help
Specifies the pager to use for help and for displaying the conformable
units.  The help function browses the units database and calls
the pager using the @samp{+n}@var{n} syntax for specifying a line
number.  The default pager is @command{more}; @env{PAGER} can be used
to specify alternatives such as @command{less}, @command{pg},
@command{emacs}, or @command{vi}.

@item UNITS_ENGLISH
@cindex UNITS_ENGLISH environment variable
@cindex environment variable, UNITS_ENGLISH
Set to either @samp{US} or
@samp{GB} to choose United States or British volume definitions,
overriding the default from your locale.

@item UNITSFILE
@cindex UNITSFILE environment variable
@cindex environment variable, UNITSFILE
Specifies the units data file to use (instead of the default).
You can only specify a single units data file using this environment
variable.  If units data files are given using the @option{-f} option,
the file specified by @env{UNITSFILE} will be not be loaded unless the
@option{-f} option is given with the empty string
(@w{@samp{units -f ""}}).

@item UNITSLOCALEMAP
@cindex UNITSLOCALEMAP environment variable
@cindex environment variable, UNITSLOCALEMAP
Windows only; this variable has no effect on Unix-like systems.
Specifies the units locale map file to use (instead of the default).
This variable seldom needs to be set, but you can use it to ensure that
the locale map file will be found if you specify a location for the
units data file using either the @option{-f} option or the
@env{UNITSFILE} environment variable, and that location does not also
contain the locale map file.

@item UNITS_SYSTEM
@cindex UNITS_SYSTEM environment variable
@cindex environment variable, UNITS_SYSTEM
This environment variable is used in the default main data file to select
CGS measurement systems.  Currently supported systems are @samp{esu},
@samp{emu}, @samp{gauss[ian]}, @samp{hlu}, @samp{natural},
@samp{natural-gauss}, @samp{planck}, @samp{planck-red}, @samp{hartree}
and @samp{si}.  The default is @samp{si}.

@end table

@node Data Files
@c =====================================================================
@chapter Data Files
@c =====================================================================
@cindex files, data
@cindex data files

The @command{units} program uses four default data files: the main data
file, @file{definitions.units}; the atomic masses of the elements,
@file{elements.units}; currency exchange rates, @file{currency.units},
and the US Consumer Price Index, @file{cpi.units}.  The last three files
are loaded by means of @samp{!include} directives in the main file
@c man (see \fIDatabase Command Syntax\fP).
@c noman
(@pxref{Database Syntax, ,Database Command Syntax}).
@c end noman
The program can
also use an optional personal units data file @file{.units}
(@file{unitdef.units} under Windows) located in the user's home
directory.  The personal units data file is described in more detail in
@ref{Units Data Files}.

On Unix-like systems, the data files are typically located in
@file{/usr/share/units} if @command{units} is provided with the
operating system, or in @file{/usr/local/share/units} if @command{units}
is compiled from the source distribution.  Note that the currency file
@file{currency.units} is a symbolic link to another location.

On systems running Microsoft Windows, the files may be in the same
locations if Unix-like commands are available, a Unix-like file
structure is present (e.g., @file{C:/usr/local}), and @command{units} is
compiled from the source distribution.  If Unix-like commands are not
available, a more common location is
@w{@file{C:\Program Files (x86)\GNU\units}} (for 64-bit Windows
installations) or @w{@file{C:\Program Files\GNU\units}} (for 32-bit
installations).

If @command{units} is obtained from the GNU Win32 Project
(@uref{http://gnuwin32.sourceforge.net/}), the files are commonly in
@w{@file{C:\Program Files\GnuWin32\share\units}}.

If the default main units data file is not an absolute pathname,
@command{units} will look for the file in the directory that contains
the @command{units} program; if the file is not found there,
@command{units} will look in a directory @code{../share/units} relative
to the directory with the @command{units} program.

You can determine the location of the files by running
@w{@samp{units --version}}.  Running @w{@samp{units --info}}
will give you additional information about the files, how
@command{units} will attempt to find them, and the status of the
related environment variables.


@node Unicode Support
@c =====================================================================
@chapter Unicode Support
@c =====================================================================
@cindex Unicode support
@cindex UTF-8
@cindex @samp{!utf8}
@cindex command, @samp{!utf8}
@cindex @samp{!endutf8}
@cindex command, @samp{!endutf8}

@menu
* Unicode Support on Windows:: Unicode support on Windows
@end menu

The standard units data file is in Unicode, using UTF-8 encoding.  Most
definitions use only ASCII characters (i.e., code points U+0000 through
U+007F); definitions using non-ASCII characters appear in blocks
beginning with @samp{!utf8} and ending with @samp{!endutf8}.

The non-ASCII definitions are loaded only if the platform and the locale
support @w{UTF-8}.  Platform support is determined when @command{units}
is compiled; the locale is checked at every invocation of
@command{units}.  To see if your version of @command{units} includes
Unicode support, invoke the program with the @option{--version} option.

When Unicode support is available, @command{units} checks every line
within UTF-8 blocks in all of the units data files for invalid or
non-printing UTF-8 sequences; if such sequences occur, @command{units}
ignores the entire line.  In addition to checking validity,
@command{units} determines the display width of non-ASCII characters to
ensure proper positioning of the pointer in some error messages and to
align columns for the @samp{search} and @samp{?} commands.

Microsoft Windows supports UTF-8 in console applications running
in Windows Terminal; UTF-8 is not supported in applications
running in the older Windows Console Host---@pxref{Unicode Support on Windows}.
The UTF-16 and UTF-32 encodings are not supported on any
platforms.

If Unicode support is available and definitions that contain non-ASCII
UTF-8 characters are added to a units data file, those definitions
should be enclosed within @samp{!utf8} @dots{} @samp{!endutf8} to ensure
that they are only loaded when Unicode support is available.  As usual,
the @samp{!} must appear as the first character on the line.  As
discussed in @ref{Units Data Files}, it's usually best to put such
definitions in supplemental data files linked by an @samp{!include}
command or in a personal units data file.

When Unicode support is not available, @command{units} makes no assumptions
about character encoding, except that characters in the range 00--7F
hexadecimal correspond to ASCII encoding.  Non-ASCII characters are
simply sequences of bytes, and have no special meanings; for definitions
in supplementary units data files, you can use any encoding consistent
with this assumption.  For example, if you wish to use non-ASCII
characters in definitions when running @command{units} under Windows,
you can use a character set such as Windows ``ANSI'' (code page 1252 in
the US and Western Europe); if this is done, the console code page must
be set to the same encoding for the characters to display properly.
You can even use UTF-8, though some messages may be improperly aligned,
and @command{units} will not detect invalid UTF-8 sequences.  If you use
UTF-8 encoding when Unicode support is not available, you should place any
definitions with non-ASCII characters @emph{outside} @samp{!utf8}
@dots{} @samp{!endutf8} blocks---otherwise, they will be ignored.

Except for code examples, typeset material usually uses the Unicode
symbols for mathematical operators.
To facilitate copying and pasting from such sources, several
typographical characters are converted to the ASCII operators
used in @command{units}:
the figure dash (U+2012),
minus (@samp{@minus{}}; U+2212),
and en dash (`--'; U+2013) are converted to the operator @samp{-};
the multiplication sign (@samp{@U{00D7}}; U+00D7),
N-ary times operator (U+2A09),
dot operator (@samp{@U{22C5}}; U+22C5),
and middle dot (@samp{@U{00B7}}; U+00B7)
are converted to the operator @samp{*};
the division sign (@samp{@U{00F7}}; U+00F7)
is converted to the operator @samp{/};
and the fraction slash (U+2044) is converted to the operator@tie{}@samp{|}.

@node Unicode Support on Windows
@c ---------------------------------------------------------------------
@section Unicode Support on Windows
@c ---------------------------------------------------------------------

Microsoft Windows supports UTF-8 in console applications running
in Windows Terminal but not in applications running in the older
Windows Console Host.  In Windows Terminal, the code page must be
set to 65001 for UTF-8 to be enabled.
With the UTF-8 code page, running @w{@code{units -V}} might show

@example
@group
GNU Units version 2.24
Without readline, with UTF-8, locale English_United States (en_US)
@end group
@end example

@noindent
Two values are shown for the locale: the first is the one
returned by the system; the second is the POSIX value to which
the system value is mapped.

With a different code page, the result might be
@example
@group
GNU Units version 2.24
Without readline, with UTF-8 (disabled), locale English_United States (en_US)
To enable UTF-8: set code page to 65001
@end group
@end example

@noindent
If @command{units} is running in Windows Console Host, regardless
of the code page, the result might be

@example
@group
GNU Units version 2.24
Without readline, with UTF-8 (disabled), locale English_United States (en_US)
To enable UTF-8: run in Windows Terminal and set code page to 65001
@end group
@end example

@noindent
The UTF-8 code page can be set by running @w{@code{chcp 65001}}.

As of late 2024, the Windows build of @command{units} does not
identify characters---typically East Asian---that occupy more than
one column, and error messages involving those characters may not
be properly aligned.

@node Readline Support
@c =====================================================================
@chapter Readline Support
@c =====================================================================
@cindex @command{readline}, use with @command{units}

If the @command{readline} package has been compiled in, then when
@command{units} is used interactively, numerous command line editing
features are available.  To check if your version of @command{units}
includes @command{readline}, invoke the program with the
@option{--version} option.

For complete information about @command{readline}, consult the
documentation for the @command{readline} package.  Without any
configuration, @command{units} will allow editing in the style of
emacs.  Of particular use with @command{units} are the completion
commands.

@cindex @samp{?} for unit completion with @command{readline}
@cindex unit completion using @samp{?} (@command{readline} only)
@cindex completion, unit, using @samp{?} (@command{readline} only)
If you type a few characters and then hit @key{ESC} followed by
@kbd{?}, then @command{units} will display a list of all the units that
start with the characters typed.  For example, if you type @kbd{metr} and
then request completion, you will see something like this:
@cindex unit name completion

@example
@group
You have: metr
metre             metriccup         metrichorsepower  metrictenth
metretes          metricfifth       metricounce       metricton
metriccarat       metricgrain       metricquart       metricyarncount
You have: metr
@end group
@end example

@noindent
If there is a unique way to complete a unit name, you can hit the @key{TAB} key
and @command{units} will provide the rest of the unit name.  If @command{units}
beeps, it means that there is no unique completion.  Pressing the @key{TAB}
key a second time will print the list of all completions.

The readline library also keeps a history of the values you enter.
You can move through this history using the up and down arrows.  The
history is saved to the file @file{.units_history} in your home
directory so that it will persist across multiple @command{units}
invocations.  If you wish to keep work for a certain project separate
you can change the history filename using the @option{--history}
option.  You could, for example, make an alias for @command{units} to
@code{units --history .units_history} so that @command{units} would
save separate history in the current directory.
The length of each history file is limited to 5000 lines.  Note also that if
you run several concurrent copies of @command{units} each one will save
its new history to the history file upon exit.

@node Currency
@c =====================================================================
@chapter Updating Currency Exchange Rates and CPI
@c =====================================================================
@cindex currency, updating
@cindex CPI, updating
@cindex exchange rates, updating

@c ---------------------------------------------------------------------
@section Currency Exchange Rates
@c ---------------------------------------------------------------------

@c man .na
The units program database includes currency exchange rates and prices
for some precious metals.  Of course, these values change over time,
sometimes very rapidly, and @command{units} cannot provide real-time
values.  To update the exchange rates, run @command{units_cur}, which
rewrites the file containing the currency rates, typically
@file{/var/lib/@/units/@/currency.units} or
@file{/usr/local/@/com/@/units/@/currency.units}
on a Unix-like system or
@file{@w{C:\Program Files (x86)}\@/GNU\@/units\@/definitions.units} on a Windows
system.
@c man .ad b

This program requires Python 3 (@uref{https://www.python.org}).
The program must be run with suitable
permissions to write the file.  To keep the rates updated automatically,
run it using a cron job on a Unix-like system, or a similar scheduling
program on a different system.

Reliable free sources of currency exchange rates have been annoyingly
ephemeral.  The program currently supports several sources:

@itemize @bullet

@item
ExchangeRate-API.com (@uref{https://www.exchangerate-api.com}). @*
The default currency server.  Allows open access without an API key,
with unlimited API requests.  Rates update once a day, the US dollar
(@samp{USD}) is the default base currency, and you can choose your
base currency with the @option{-b} option described below.  You can
optionally sign up for an API key to access paid benefits such as
faster data update rates.

@item
FloatRates (@uref{https://www/floatrates.com}). @*
The US dollar (@samp{USD}) is the default base currency.  You can
change the base currency with the
@option{-b} option described below.  Allowable base currencies are listed on
the FloatRates website.  Exchange rates update daily.

@item
The European Central Bank (@uref{https://www.ecb.europa.eu}). @*
The base currency is always the euro (@samp{EUR}).  Exchange rates
update daily.  This source offers a more limited list of currencies
than the others.

@item
Fixer (@uref{https://fixer.io}). @*
Registration for a free API key is required.  With a free API key, base
currency is the euro; exchange rates are updated hourly, the
service has a limit of 1,000 API calls per month, and SSL encryption
(https protocol) is not available.  Most of these restrictions are
eliminated or reduced with paid plans.

@item
open exchange rates (@uref{https://openexchangerates.org}). @*
Registration for a free API key is required.  With a free API key, the
base currency is the US dollar; exchange rates are updated hourly, and
there is a limit of 1,000 API calls per month.  Most of these
restrictions are eliminated or reduced with paid plans.


@end itemize

@noindent
The default source is FloatRates; you can select a different one using
@option{-s} option described below.

Precious metals pricing is obtained from Packetizer
(@uref{www.packetizer.com}).  This site updates once per day.

@c ---------------------------------------------------------------------
@section US Consumer Price Index
@c ---------------------------------------------------------------------

The @command{units} program includes the US Consumer Price Index (CPI)
published by the US Bureau of Labor Statistics: specifically, the
Consumer Price Index for All Urban Consumers (CPI-U), not seasonally
adjusted---Series CUUR0000SA0.  The @command{units_cur} command updates
the CPI and saves the result in @file{cpi.units} in the same location as
@file{currency.units}.  The data are obtained via the BLS Public Data
API (@uref{https://www.bls.gov/developers/}).  These data update once a
month.  When @command{units_cur} runs it will only attempt to update the
CPI data if the current CPI data file is from a previous month, or if
the current date is after the 18th of the month.

@c ---------------------------------------------------------------------
@section Invoking @command{units_cur}
@c ---------------------------------------------------------------------

You invoke @command{units_cur} like this:

@example
units_cur [@var{options}] [@var{currency_file}] [@var{cpi_file}]
@end example

@noindent
By default, the output is written to the default currency and CPI files
described above; this is usually what you want, because this is where
@command{units} looks for the files.  If you wish, you can specify
different filenames on the command line and @command{units_cur} will
write the data to those files.  If you give @samp{-} for a file it will
write to standard output.

@noindent
The following options are available:

@table @env
@item -h
@itemx --help
Print a summary of the options for @command{units_cur}.

@item -V
@itemx --version
Print the @command{units_cur} version number.

@item -v
@itemx --verbose
Give slightly more verbose output when attempting to update currency
exchange rates.

@item -s @var{source}
@itemx --source @var{source}
Specify the source for currency exchange rates; currently supported
values are @samp{floatrates} (for FloatRates), @samp{eubank} (for the
European Central Bank), @samp{fixer} (for Fixer), and
@samp{openexchangerates} (for open exchange rates); the last two require
an API key to be given with the @option{-k} option.

@item -b @var{base}
@itemx --base @var{base}
Set the base currency (when allowed by the site providing the data).
@var{base} should be a 3-letter ISO currency code, e.g., @samp{USD}.
The specified currency will be the primitive currency unit used by
@command{units}.  You may find it convenient to specify your local
currency.  Conversions may be more accurate and you will be able to
convert to your currency by simply hitting @key{Enter} at the
@w{@samp{You want:}} prompt.  This option is ignored if the source
does not allow specifying the base currency.  (Currently only
floatrates supports this option.)

@item -k @var{key}
@itemx --key @var{key}
Set the API key to @var{key} for currency sources that require it.

@item --blskey @var{BLSkey}
Set the US Bureau of Labor Statistics (BLS) key for fetching CPI data.
Without a BLS key you should be able to fetch the CPI data exactly one
time per day.  If you want to use a key you must request a personal
key from BLS.  

@end table

@node Database Syntax
@c =====================================================================
@chapter Database Command Syntax
@c =====================================================================
@cindex database syntax summary
@cindex syntax of units database
@cindex commands in units database

@table @t
@item @var{unit} @var{definition}
Define a regular unit.

@item @var{prefix}- @var{definition}
Define a prefix.

@item @var{funcname}(@var{var}) noerror units=[@var{in-units},@var{out-units}] domain=[@var{x1},@var{x2}] range=[@var{y1},@var{y2}] @var{definition(var)} ; @var{inverse(funcname)}
Define a nonlinear unit or unit function.  The four optional keywords @command{noerror},
@samp{units=}, @samp{range=} and @samp{domain=} can appear in
any order.  The definition of the inverse is optional.

@item @var{tabname}[@var{out-units}] noerror @var{pair-list}
Define a piecewise linear unit.  The pair list gives the points on the
table listed in ascending order.  The @command{noerror} keyword is
optional.

@item !endlocale
End a block of definitions beginning with @samp{!locale}

@item !endutf8
End a block of definitions begun with @samp{!utf8}

@item !endvar
End a block of definitions begun with @samp{!var} or @samp{!varnot}

@item !include @var{file}
Include the specified file.

@item !locale @var{value}
Load the following definitions only of the locale is set to
@var{value}.

@item !message @var{text}
Display @var{text} when the database is read unless the quiet
option (@option{-q}) is enabled.  If you omit @var{text}, then units
will display a blank line.  Messages will also appear in the log
file.

@item !prompt @var{text}
Prefix the @w{@samp{You have:}} prompt with the specified text.  If
you omit @var{text}, then any existing prefix is canceled.

@item !set @var{variable} @var{value}
Sets the environment variable, @var{variable}, to the specified
value @emph{only if} it is not already set.

@item !unitlist @var{alias} @var{definition}
Define a unit list alias.

@item !utf8
Load the following definitions only if @command{units} is running with
UTF-8 enabled.

@item !var @var{envar} @var{value-list}
Load the block of definitions that follows only if the environment
variable @var{envar} is set to one of the values listed in the
space-separated value list.  If @var{envar} is not set,
@command{units} prints an error message and ignores the block of
definitions.

@item !varnot @var{envar} @var{value-list}
Load the block of definitions that follows only if the environment
variable @var{envar} is set to value that is @emph{not} listed in the
space-separated value list.  If @var{envar} is not set, @command{units}
prints an error message and ignores the block of definitions.

@end table

@node GNU Free Documentation License
@c =====================================================================
@chapter GNU Free Documentation License
@c =====================================================================
@include fdl-1.3.texi

@node Index
@unnumbered Index

@printindex cp
@bye

@c man .\" ====================================================================
@c man .SH FILES
@c man .\" ====================================================================
@c man @DATAFILE@ \(em the standard units data file
@c man .\" ====================================================================
@c man .SH AUTHOR
@c man .\" ====================================================================
