Provided by: units_2.21-2_amd64 
NAME
units — unit conversion and calculation program
SYNOPSIS
[options] [from-unit [to-unit]]
DESCRIPTION
The 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 Celsius; see Temperature Conversions. The program can also perform conversions from
and to sums of units, such as converting between meters and feet plus inches.
Basic operation is simple: you enter the units that you want to convert from and the units
that you want to convert to. You can use the program interactively with prompts, or you
can use it from the command line.
Beyond simple unit conversions, 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, see Complicated Unit Expressions.
The units are defined in an external data file. You can use the extensive data file that
comes with this 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 file.
You can change the default behavior of units with various options given on the command
line. See Invoking Units for a description of the available options.
INTERACTING WITH UNITS
To invoke units for interactive use, type units at your shell prompt. The program will
print something like this:
Currency exchange rates from www.timegenie.com on 2014-03-05
2860 units, 109 prefixes, 85 nonlinear units
You have:
At the ‘You have:’ prompt, type the quantity and units that you are converting from. For
example, if you want to convert ten meters to feet, type 10 meters. Next, units will
print ‘You want:’. You should type the units you want to convert to. To convert to feet,
you would type feet. If the readline library was compiled in, then tab will complete unit
names. See Readline Support for more information about readline. To quit the program type
quit or exit at either prompt.
The result will be displayed in two ways. The first line of output, which is marked with
a ‘*’ to indicate multiplication, gives the result of the conversion you have asked for.
The second line of output, which is marked with a ‘/’ to indicate division, gives the
inverse of the conversion factor. If you convert 10 meters to feet, units will print
* 32.808399
/ 0.03048
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 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:
You have: grains
You want: pounds
* 0.00014285714
/ 7000
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 ‘--verbose’ option:
You have: grain
You want: aeginamina
grain = 0.00010416667 aeginamina
grain = (1 / 9600) aeginamina
If you request a conversion between units that measure reciprocal dimensions, then units
will display the conversion results with an extra note indicating that reciprocal
conversion has been done:
You have: 6 ohms
You want: siemens
reciprocal conversion
* 0.16666667
/ 6
Reciprocal conversion can be suppressed by using the ‘--strict’ option. As usual, use the
‘--verbose’ option to get more comprehensible output:
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
If you enter incompatible unit types, the units program will print a message indicating
that the units are not conformable and it will display the reduced form for each unit:
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
If you only want to find the reduced form or definition of a unit, simply press Enter at
the ‘You want:’ prompt. Here is an example:
You have: jansky
You want:
Definition: fluxunit = 1e-26 W/m^2 Hz = 1e-26 kg / s^2
The output from 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.
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.
You have: (14 ft lbf) (12 radians/sec)
You want: watts
* 227.77742
/ 0.0043902509
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:
You have: cuberoot(G earthmass / (circle/siderealday)^2) - earthradius
You want: miles
* 22243.267
/ 4.4957425e-05
Named dimensionless units are not treated as dimensionless in other contexts. They cannot
be used as exponents so for example, ‘meter^radian’ is forbidden.
If you want a list of options you can type ? at the ‘You want:’ prompt. The program will
display a list of named units that are conformable with the unit that you entered at the
‘You have:’ prompt above. Conformable unit combinations will not appear on this list.
Typing help at either prompt displays a short help message. You can also type help
followed by a unit name. This will invoke a pager on the units data base 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. (You can generally quit out of the page
by pressing ‘q’.)
Typing search text will display a list of all of the units whose names contain text as a
substring along with their definitions. This may help in the case where you aren't sure
of the right unit name.
USING UNITS NON-INTERACTIVELY
The 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
units "2 liters" quarts
then units will print
* 2.1133764
/ 0.47317647
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.
units does not require a space between a numerical value and the unit, so the previous
example can be given as
units 2liters quarts
to avoid having to quote the first argument.
If the conversion is successful, units will return success (zero) to the calling
environment. If you enter non-conformable units, then units will print a message giving
the reduced form of each unit and it will return failure (nonzero) to the calling
environment.
If the ‘--conformable’ option is given, only one unit expression is allowed, and units
will print all units conformable with that expression; it is equivalent to giving ? at the
‘You want:’ prompt. For example,
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
If you give more than one unit expression with the ‘--conformable’ option, the program
will exit with an error message and return failure. This option has no effect in
interactive mode.
If the ‘--terse’ (‘-t’) option is given with the ‘--conformable’ option, conformable units
are shown without definitions; with the previous example, this would give
units --terse --conformable gauss
B_FIELD
Gs
T
gauss
stT
statT
stattesla
tesla
When the ‘--conformable’ option is not given and you invoke units with only one argument,
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.
UNIT DEFINITIONS
The conversion information is read from a units data file that is called
‘definitions.units’ and is usually located in the ‘/usr/share/units’ directory. If you
invoke units with the ‘-V’ option, it will print the location of this file. The default
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.,
‘seventeen’) are recognized.
Many constants of nature are defined, including these:
pi ratio of circumference to diameter
c speed of light
e charge on an electron
force acceleration of gravity
mole Avogadro's number
water pressure per unit height of water
Hg pressure per unit height of mercury
au astronomical unit
k Boltzman's constant
mu0 permeability of vacuum
epsilon0 permittivity of vacuum
G Gravitational constant
mach speed of sound
The standard data file includes atomic masses for all of the elements and numerous other
constants. Also included are the densities of various ingredients used in baking so that
‘2 cups flour_sifted’ can be converted to ‘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.
The ‘pound’ is a unit of mass. To get force, multiply by the force conversion unit
‘force’ or use the shorthand ‘lbf’. (Note that ‘g’ is already taken as the standard
abbreviation for the gram.) The unit ‘ounce’ is also a unit of mass. The fluid ounce is
‘fluidounce’ or ‘floz’. When British capacity units differ from their US counterparts,
such as the British Imperial gallon, the unit is defined both ways with ‘br’ and ‘us’
prefixes. Your locale settings will determine the value of the unprefixed unit. Currency
is prefixed with its country name: ‘belgiumfranc’, ‘britainpound’.
When searching for a unit, if the specified string does not appear exactly as a unit name,
then the units program will try to remove a trailing ‘s’, ‘es’. Next units will replace a
trailing ‘ies’ with ‘y’. If that fails, units will check for a prefix. The database
includes all of the standard metric prefixes. Only one prefix is permitted per unit, so
‘micromicrofarad’ will fail. However, prefixes can appear alone with no unit following
them, so ‘micro*microfarad’ will work, as will ‘micro microfarad’.
To find out which units and prefixes are available, read the standard units data file,
which is extensively annotated.
English Customary Units
English customary units differ in various ways in 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 units runs in the ‘en_GB’ locale you will
get the British volume measures. If it runs in the ‘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 UNITS_ENGLISH to either
‘US’ or ‘GB’ to set the desired definitions independent of the locale.
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 yard = 0.9144 m (exactly), which was approximately halfway between the values
used by the UK and the US; it had the additional advantage of making 1 inch = 2.54 cm
(exactly). This new standard was termed the 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, and link) in terms of the previous value for the foot, which was termed the US survey
foot. The US defined a US survey mile as 5280 US survey feet, and defined a statute mile
as a US survey mile. The US values for these units differ from the international values
by about 2 ppm.
The units program uses the international values for these units; the US values can be
obtained by using either the ‘US’ or the ‘survey’ prefix. In either case, the simple
familiar relationships among the units are maintained, e.g., 1 ‘furlong’ = 660 ‘ft’, and 1
‘USfurlong’ = 660 ‘USft’, though the metric equivalents differ slightly between the two
cases. The ‘US’ prefix or the ‘survey’ prefix can also be used to obtain the US survey
mile and the value of the US yard prior to 1959, e.g., ‘USmile’ or ‘surveymile’ (but not
‘USsurveymile’). To get the US value of the statute mile, use either ‘USstatutemile’ or
‘USmile’.
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:
You have: 100 surveymile - 100 mile
You want: inch
* 12.672025
/ 0.078913984
The pre-1959 UK values for these units can be obtained with the prefix ‘UK’.
In the US, the acre is officially defined in terms of the US survey foot, but units uses a
definition based on the international foot. If you want the official US acre use ‘USacre’
and similarly use ‘USacrefoot’ for the official US version of that unit. The difference
between these units is about 4 parts per million.
UNIT EXPRESSIONS
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 units is invoked with its
default options. Additionally, units supports some extensions, including high priority
multiplication using a space, and a high priority numerical division operator (‘|’) that
can simplify some expressions.
You multiply units using a space or an asterisk (‘*’). The next example shows both forms:
You have: arabicfoot * arabictradepound * force
You want: ft lbf
* 0.7296
/ 1.370614
You can divide units using the slash (‘/’) or with ‘per’:
You have: furlongs per fortnight
You want: m/s
* 0.00016630986
/ 6012.8727
You can use parentheses for grouping:
You have: (1/2) kg / (kg/meter)
You want: league
* 0.00010356166
/ 9656.0833
White space surrounding operators is optional, so the previous example could have used
‘(1/2)kg/(kg/meter)’. As a consequence, however, hyphenated spelled-out numbers (e.g.,
‘forty-two’) cannot be used; ‘forty-two’ is interpreted as ‘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 ‘/’ 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: ‘J / mol K’. The ‘*’ and ‘/’ operators have the same
precedence, and are evaluated left to right; if you multiply with ‘*’, you must group the
terms in the denominator with parentheses: ‘J / (mol * K)’.
The higher precedence of the space operator may not always be advantageous. For example,
‘m/s s/day’ is equivalent to ‘m / s s day’ and has dimensions of length per time cubed.
Similarly, ‘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: ‘(1/2) meter’. The ‘*’ operator is convenient for
multiplying a sequence of quotients. For example, ‘m/s * s/day’ is equivalent to ‘m/day’.
Similarly, you could write ‘1/2 * meter’ to get half a meter.
The units program supports another option for numerical fractions: you can indicate
division of numbers with the vertical bar (‘|’), so if you wanted half a meter you could
write ‘1|2 meter’. You cannot use the vertical bar to indicate division of non-numerical
units (e.g., ‘m|s’ results in an error message).
Powers of units can be specified using the ‘^’ character, as shown in the following
example, or by simple concatenation of a unit and its exponent: ‘cm3’ is equivalent to
‘cm^3’; if the exponent is more than one digit, the ‘^’ is required. You can also use
‘**’ as an exponent operator.
You have: cm^3
You want: gallons
* 0.00026417205
/ 3785.4118
Concatenation only works with a single unit name: if you write ‘(m/s)2’, units will treat
it as multiplication by 2. When a unit includes a prefix, exponent operators apply to the
combination, so ‘centimeter3’ gives cubic centimeters. If you separate the prefix from
the unit with any multiplication operator (e.g., ‘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 ‘centi * (meter^3)’, and gives a hundredth of a cubic
meter, not a cubic centimeter. The units program is limited internally to products of 99
units; accordingly, expressions like ‘meter^100’ or ‘joule^34’ (represented internally as
‘kg^34 m^68 / s^68’) will fail.
The ‘|’ operator has the highest precedence, so you can write the square root of two
thirds as ‘2|3^1|2’. The ‘^’ operator has the second highest precedence, and is evaluated
right to left, as usual:
You have: 5 * 2^3^2
You want:
Definition: 2560
With a dimensionless base unit, any dimensionless exponent is meaningful (e.g.,
‘pi^exp(2.371)’). Even though angle is sometimes treated as dimensionless, exponents
cannot have dimensions of angle:
You have: 2^radian
^
Exponent not dimensionless
If the base unit is not dimensionless, the exponent must be a rational number p/q, and the
dimension of the unit must be a power of q, so ‘gallon^2|3’ works but ‘acre^2|3’ fails.
An exponent using the slash (‘/’) operator (e.g., ‘gallon^(2/3)’) is also acceptable; the
parentheses are needed because the precedence of ‘^’ is higher than that of ‘/’. Since
units cannot represent dimensions with exponents greater than 99, a fully reduced exponent
must have q < 100. When raising a non-dimensionless unit to a power, units attempts to
convert a decimal exponent to a rational number with q < 100. If this is not possible
units displays an error message:
You have: ft^1.234
Base unit not dimensionless; rational exponent required
A decimal exponent must match its rational representation to machine precision, so
‘acre^1.5’ works but ‘gallon^0.666’ does not.
Sums and Differences of Units
You may sometimes want to add values of different units that are outside the SI. You may
also wish to use units as a calculator that keeps track of units. Sums of conformable
units are written with the ‘+’ character, and differences with the ‘-’ character.
You have: 2 hours + 23 minutes + 32 seconds
You want: seconds
* 8612
/ 0.00011611705
You have: 12 ft + 3 in
You want: cm
* 373.38
/ 0.0026782366
You have: 2 btu + 450 ft lbf
You want: btu
* 2.5782804
/ 0.38785542
The expressions that are added or subtracted must reduce to identical expressions in
primitive units, or an error message will be displayed:
You have: 12 printerspoint - 4 heredium
^
Illegal sum of non-conformable units
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.
You have: lightyear + cm
No warning is given, however. As usual, the precedence for ‘+’ and ‘-’ is lower than that
of the other operators. A fractional quantity such as 2 1/2 cups can be given as ‘(2+1|2)
cups’; the parentheses are necessary because multiplication has higher precedence than
addition. If you omit the parentheses, units attempts to add ‘2’ and ‘1|2 cups’, and you
get an error message:
You have: 2+1|2 cups
^
Illegal sum or difference of non-conformable units
The expression could also be correctly written as ‘(2+1/2) cups’. If you write ‘2 1|2
cups’ the space is interpreted as multiplication so the result is the same as ‘1 cup’.
The ‘+’ and ‘-’ characters sometimes appears in exponents like ‘3.43e+8’. This leads to
an ambiguity in an expression like ‘3e+2 yC’. The unit ‘e’ is a small unit of charge, so
this can be regarded as equivalent to ‘(3e+2) yC’ or ‘(3 e)+(2 yC)’. This ambiguity is
resolved by always interpreting ‘+’ and ‘-’ as part of an exponent if possible.
Numbers as Units
For 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:
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
And the second example shows how the dollar sign in the units conversion can precede the
five. Be careful: units will interpret ‘$5’ with no space as equivalent to ‘dollar^5’.
Built-in Functions
Several built-in functions are provided: ‘sin’, ‘cos’, ‘tan’, ‘asin’, ‘acos’, ‘atan’,
‘sinh’, ‘cosh’, ‘tanh’, ‘asinh’, ‘acosh’, ‘atanh’, ‘exp’, ‘ln’, ‘log’, ‘abs’, ‘round’,
‘floor’, ‘ceil’, ‘factorial’, ‘Gamma’, ‘lnGamma’, ‘erf’, and ‘erfc’; the function
‘lnGamma’ is the natural logarithm of the ‘Gamma’ function.
The ‘sin’, ‘cos’, and ‘tan’ functions require either a dimensionless argument or an
argument with dimensions of angle.
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
The other functions on the list require dimensionless arguments. The inverse
trigonometric functions return arguments with dimensions of angle.
The ‘ln’ and ‘log’ functions give natural log and log base 10 respectively. To obtain
logs for any integer base, enter the desired base immediately after ‘log’. For example,
to get log base 2 you would write ‘log2’ and to get log base 47 you could write ‘log47’.
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
If you wish to take roots of units, you may use the ‘sqrt’ or ‘cuberoot’ functions. These
functions require that the argument have the appropriate root. You can obtain higher
roots by using fractional exponents:
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
Previous Result
You can insert the result of the previous conversion using the underscore (‘_’). It is
useful when you want to convert the same input to several different units, for example
You have: 2.3 tonrefrigeration
You want: btu/hr
* 27600
/ 3.6231884e-005
You have: _
You want: kW
* 8.0887615
/ 0.12362832
Suppose you want to do some deep frying that requires an oil depth of 2 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 ‘circlearea’ gives the radius of the circle (see Other
Nonlinear Units, for a more detailed description) in SI units; you want the diameter in
inches:
You have: 1|2 gallon / 2 in
You want: circlearea
0.10890173 m
You have: 2 _
You want: in
* 8.5749393
/ 0.1166189
In most cases, surrounding white space is optional, so the previous example could have
used ‘2_’. If ‘_’ follows a non-numerical unit symbol, however, the space is required:
You have: m_
^
Parse error
When ‘_’ is followed by a digit, the operation is multiplication rather than
exponentiation, so that ‘_2’, is equivalent to ‘_ * 2’ rather than ‘_^2’.
You can use the ‘_’ symbol any number of times; for example,
You have: m
You want:
Definition: 1 m
You have: _ _
You want:
Definition: 1 m^2
Using ‘_’ before a conversion has been performed (e.g., immediately after invocation)
generates an error:
You have: _
^
No previous result; '_' not set
Accordingly, ‘_’ serves no purpose when units is invoked non-interactively.
If units is invoked with the ‘--verbose’ option (see Invoking Units), the value of ‘_’ is
not expanded:
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
You can give ‘_’ at the ‘You want:’ prompt, but it usually is not very useful.
Complicated Unit Expressions
The units program is especially helpful in ensuring accuracy and dimensional consistency
when converting lengthy unit expressions. For example, one form of the Darcy-Weisbach
fluid-flow equation is
Delta P = (8 / pi)^2 (rho fLQ^2) / d^5,
where Delta P is the pressure drop, rho is the mass density, f is the (dimensionless)
friction factor, L is the length of the pipe, Q is the volumetric flow rate, and d is the
pipe diameter. It might be desired to have the equation in the form
Delta P = A1 rho fLQ^2 / d^5
that accepted the user’s normal units; for typical units used in the US, the required
conversion could be something like
You have: (8/pi^2)(lbm/ft^3)ft(ft^3/s)^2(1/in^5)
You want: psi
* 43.533969
/ 0.022970568
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
‘*’ rather than a space; then parentheses are needed only around ‘ft^3/s’ because of its
exponent:
You have: 8/pi^2 * lbm/ft^3 * ft * (ft^3/s)^2 /in^5
You want: psi
* 43.533969
/ 0.022970568
Without parentheses, and using spaces for multiplication, the previous conversion would
need to be entered as
You have: 8 lb ft ft^3 ft^3 / pi^2 ft^3 s^2 in^5
You want: psi
* 43.533969
/ 0.022970568
Backwards Compatibility: ‘*’ and ‘-’
The original 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 (‘*’) included in this units program has, by default, the same
precedence as division, and hence follows the usual precedence rules. For backwards
compatibility you can invoke units with the ‘--oldstar’ option. Then ‘*’ has a higher
precedence than division, and the same precedence as multiplication using the space.
Historically, the hyphen (‘-’) has been used in technical publications to indicate
products of units, and the original units program treated it as a multiplication operator.
Because units provides several other ways to obtain unit products, and because ‘-’ is a
subtraction operator in general algebraic expressions, units treats the binary ‘-’ as a
subtraction operator by default. For backwards compatibility use the ‘--product’ option,
which causes units to treat the binary ‘-’ operator as a product operator. When ‘-’ is a
multiplication operator it has the same precedence as multiplication with a space, giving
it a higher precedence than division.
When ‘-’ is used as a unary operator it negates its operand. Regardless of the units
options, if ‘-’ appears after ‘(’ or after ‘+’, then it will act as a negation operator.
So you can always compute 20 degrees minus 12 minutes by entering ‘20 degrees +
-12 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.
NONLINEAR UNIT CONVERSIONS
Nonlinear units are represented using functional notation. They make possible nonlinear
unit conversions such as temperature.
Temperature Conversions
Conversions between temperatures are different from linear conversions between temperature
increments—see the example below. The absolute temperature conversions are handled by
units starting with ‘temp’, and you must use functional notation. The temperature-
increment conversions are done using units starting with ‘deg’ and they do not require
functional notation.
You have: tempF(45)
You want: tempC
7.2222222
You have: 45 degF
You want: degC
* 25
/ 0.04
Think of ‘tempF(x)’ not as a function but as a notation that indicates that x should have
units of ‘tempF’ attached to it. See 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 ‘tempF(x)’ is to absolute temperature, so that
You have: tempF(45)
You want: degR
* 504.67
/ 0.0019814929
gives the same result as
You have: tempF(45)
You want: tempR
* 504.67
/ 0.0019814929
But if you convert ‘tempF(x)’ to ‘degC’, the output is probably not what you expect:
You have: tempF(45)
You want: degC
* 280.37222
/ 0.0035666871
The result is the temperature in K, because ‘degC’ is defined as ‘K’, the Kelvin. For
consistent results, use the ‘tempX’ units when converting to a temperature rather than
converting a temperature increment.
The ‘tempC()’ and ‘tempF()’ definitions are limited to positive absolute temperatures, and
giving a value that would result in a negative absolute temperature generates an error
message:
You have: tempC(-275)
^
Argument of function outside domain
Other Nonlinear Units
Some other examples of nonlinear units are numerous different ring sizes and wire gauges,
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.
Wire gauges with multiple zeroes are signified using negative numbers where two zeroes is
‘-1’. Alternatively, you can use the synonyms ‘g00’, ‘g000’, and so on that are defined
in the standard units data file.
You have: wiregauge(11)
You want: inches
* 0.090742002
/ 11.020255
You have: brwiregauge(g00)
You want: inches
* 0.348
/ 2.8735632
You have: 1 mm
You want: wiregauge
18.201919
You have: grit_P(600)
You want: grit_ansicoated
342.76923
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.
You can compute the area of a circle using the nonlinear unit, ‘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.
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
The inverse of a nonlinear conversion is indicated by prefixing a tilde (‘~’) to the
nonlinear unit name:
You have: ~wiregauge(0.090742002 inches)
You want:
Definition: 11
You can give a nonlinear unit definition without an argument or parentheses, and press
Enter at the ‘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:
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
To see the definition of the inverse use the ‘~’ notation. In this case the parameter in
the functional definition will usually be the name of the unit. Note that the inverse for
‘tempC’ shows that it requires units of ‘K’ in the specification of the allowed range of
values. Nonlinear unit conversions are described in more detail in Defining Nonlinear
Units.
UNIT LISTS: CONVERSION TO SUMS OF UNITS
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 from sums of units was described in
Sums and Differences of Units, and is a simple matter of adding the units with the ‘+’
sign:
You have: 12 ft + 3 in + 3|8 in
You want: ft
* 12.28125
/ 0.081424936
Although you can similarly write a sum of units to convert 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:
You have: 12.28125 ft
You want: ft + in + 1|8 in
* 11.228571
/ 0.089058524
The unit expression given at the ‘You want:’ prompt is equivalent to asking for conversion
to multiples of ‘1 ft + 1 in + 1|8 in’, which is 1.09375 ft, so the conversion in the
previous example is equivalent to
You have: 12.28125 ft
You want: 1.09375 ft
* 11.228571
/ 0.089058524
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 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 (‘;’) character:
You have: 12.28125 ft
You want: ft;in;1|8 in
12 ft + 3 in + 3|8 in
The conversion always gives integer coefficients on the units in the list, except possibly
the last unit when the conversion is not exact:
You have: 12.28126 ft
You want: ft;in;1|8 in
12 ft + 3 in + 3.00096 * 1|8 in
The order in which you list the units is important:
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
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 ‘;’ has the same effect as repeating the last unit
on the list, so ‘ft;in;1|8 in;’ is equivalent to ‘ft;in;1|8 in;1|8 in’. With the example
above, this gives
You have: 12.28126 ft
You want: ft;in;1|8 in;
12 ft + 3 in + 3|8 in + 0.00096 * 1|8 in
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 ‘--round’ (‘-r’) option. With the previous example, the result is
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)
When you use the ‘-r’ option, repeating the last unit on the list has no effect (e.g.,
‘ft;in;1|8 in;1|8 in’ is equivalent to ‘ft;in;1|8 in’), and hence neither does ending a
list with a ‘;’. With a single unit and the ‘-r’ option, a terminal ‘;’ does have an
effect: it causes units to treat the single unit as a list and produce a rounded value for
the single unit. Without the extra ‘;’, the ‘-r’ option has no effect on single unit
conversions. This example shows the output using the ‘-r’ option:
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)
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 ‘You have:’ prompt.
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
In the first case, units reports the disagreement between units appearing on the list. In
the second case, 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:
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
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 oz, but have only metric calibration
weights. You might try
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
You might then place one each of the 20 g, 5 g, 2 g, and 1 g weights on the scale and hope
that it indicates close to
You have: 20 g + 5 g + 2 g + 1 g
You want: oz;
0.98767093 oz
Appending ‘;’ to ‘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.,
You have: lightyear
You want: mile;100 inch;10 inch;mm;micron
5.8786254e+12 mile + 390 * 100 inch (at 15-digit precision limit)
Cooking Measure
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 1/2 cups of
an ingredient, you might wish to know the measurements in terms of measuring devices you
have available, you could use units and enter
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
By default, if a unit in a list begins with fraction of the form 1|x and its multiplier is
an integer, the fraction is given as the product of the multiplier and the numerator; for
example,
You have: 12.28125 ft
You want: ft;in;1|8 in;
12 ft + 3 in + 3|8 in
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 1/4 cup of an ingredient, but you
want a portion for 2, and your 1-cup measure is not available; you might try
You have: (5+1|4) cup / 3
You want: 1|2 cup;1|3 cup;1|4 cup
3|2 cup + 1|4 cup
This result might be fine for a baker who has a 1 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
‘--show-factor’ option, the factor will not be combined with a unity numerator, so that
you get
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
A user-specified fractional unit with a numerator other than 1 is never overridden,
however—if a unit list specifies ‘3|4 cup;1|2 cup’, a result equivalent to 1 1/2 cups will
always be shown as ‘2 * 3|4 cup’ whether or not the ‘--show-factor’ option is given.
Unit List Aliases
A unit list such as
cup;1|2 cup;1|3 cup;1|4 cup;tbsp;tsp;1|2 tsp;1|4 tsp
can be tedious to enter. The units program provides shorthand names for some common
combinations:
hms hours, minutes, seconds
dms angle: degrees, minutes, seconds
time years, days, hours, minutes and seconds
usvol US cooking volume: cups and smaller
ftin feet, inches and 1/8 inches
inchfine inches subdivided to 1/64 inch
Using these shorthands, or unit list aliases, you can do the following conversions:
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
You can define your own unit list aliases; see Defining Unit List Aliases.
You cannot combine a unit list alias with other units: it must appear alone at the
‘You want:’ prompt.
You can display the definition of a unit list alias by entering it at the ‘You have:’
prompt:
You have: dms
Definition: unit list, deg;arcmin;arcsec
When you specify compact output with ‘--compact’, ‘--terse’ or ‘-t’ and perform conversion
to a unit list, units lists the conversion factors for each unit in the list, separated by
semicolons.
You have: year
You want: day;min;sec
365;348;45.974678
Unlike the case of regular output, zeros are included in this output list:
You have: liter
You want: cup;1|2 cup;1|4 cup;tbsp
4;0;0;3.6280454
ALTERNATIVE UNIT SYSTEMS
CGS Units
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., 1 m = 100 cm). Conversions involving
electromagnetic units are more complicated, and 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 delim $$ r:
F = k_C q_1 q_2 / r^2.
Ampere’s law gives the electromagnetic force per unit length between two current-carrying
conductors separated by a distance r:
F/l = 2 k_A I_1 I_2 / r.
The two constants, k_C and k_A, are related by the square of the speed of light:
k_A = k_C / c^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 4{pi} 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 4{pi} appears in Coulomb’s law instead; this
system differs from the Gaussian system by factors of the square root of 4{pi}
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 correspondence between these units. The units program defines the units so
that you can convert between corresponding units in the various systems.
The CGS definitions involve cm^(1/2) and g^(1/2), which is problematic because units does
not normally support fractional roots of base units. The ‘--units’ (‘-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: ‘sqrt_cm’ and ‘sqrt_g’. The centimeter then
becomes ‘sqrt_cm^2’ and the gram, ‘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 ‘--units’ option are ‘gauss[ian]’, ‘esu’, ‘emu’, ‘lhu’;
the argument is case insensitive. You can also give ‘si’ which just enforces the default
SI mode and displays ‘(SI)’ at the ‘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 units uses SI units.
The changes resulting from the ‘--units’ option are actually controlled by the
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 ‘--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 UNITS_SYSTEM to ‘gaussian’ and
specify SI with the ‘--units’ option. Unlike the argument to the ‘--units’ option, the
value of UNITS_SYSTEM is case sensitive, so setting a value of ‘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.
The ESU system derives the electromagnetic units from its unit of charge, the statcoulomb,
which is defined from Coulomb’s law. The statcoulomb equals dyne^(1/2) cm, or
cm^(3/2) g^(1/2) s^(−1). The unit of current, the statampere, is 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 ‘stat-’, e.g.,
‘statvolt’ or ‘statV’. The prefix ‘st-’ is also recognized (e.g., ‘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 dyne^(1/2), or
cm^(1/2) g^(1/2) s^(−1). delim off The unit of charge, the abcoulomb, is 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 ‘ab-’, e.g.,
‘abvolt’ or ‘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., ‘statC’, ‘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,
‘hlu_charge’, ‘hlu_current’, ‘hlu_volt’, ‘hlu_efield’ and ‘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.
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 correspondence between the units in the different
systems, and units supports conversions between corresponding units. When running with
SI, units defines all of the CGS units in terms of SI. When you select a CGS system,
units defines the SI units and the other CGS system units in terms of the system you have
selected.
(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
In the above example, 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 E field and 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, units
defines various dimension units such as LENGTH, TIME, and CHARGE to be the appropriate
dimension in SI. The electromagnetic dimensions such as B_FIELD or 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.
(Gaussian) You have: statV/cm
You want: E_FIELD
* 29979.246
/ 3.335641e-05
(Gaussian) You have: statV/cm
You want: B_FIELD
* 0.0001
/ 10000
(Gaussian) You have: statV/cm
You want: H_FIELD
* 79.577472
/ 0.012566371
(Gaussian) You have: statV/cm
You want: D_FIELD
* 2.6544187e-07
/ 3767303.1
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.
(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
Natural Units
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 my 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 ‘--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 ‘natural’ and ‘natural-gauss’ respectively.
For conversions in SI mode, several unit names starting with ‘natural’ are available.
This “natural” system is defined by setting {hbar}, 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 units supports two. Both supported
forms are rationalized, in that factors of 4{pi} 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 c, {hbar}, and Boltzman’s constant are
set to 1, but in this system, Newton’s gravitational constant, G is also fixed. In the
“reduced” Planck system, delim $$ 8{pi}G = 1 whereas in the unreduced system G = 1. The
reduced system eliminates factors of 8{pi} delim off 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 ‘planck’ and for the
reduced Planck units, ‘planck-red’. Units such as ‘planckenergy’ and ‘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 ‘--units’ option use the name ‘hartree’.
Prompt Prefix
If a unit system is specified with the ‘--units’ option, the selected system’s name is
prepended to the ‘You have:’ prompt as a reminder, e.g.,
(Gaussian) You have: stC
You want:
Definition: statcoulomb = sqrt(dyne) cm = 1 sqrt_cm^3 sqrt_g / s
You can suppressed the prefix by including a line
!prompt
with no argument in a site or personal units data file. The prompt can be conditionally
suppressed by including such a line within ‘!var’ ... ‘!endvar’ constructs, e.g.,
!var UNITS_SYSTEM gaussian gauss
!prompt
!endvar
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.
LOGGING CALCULATIONS
The ‘--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 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
# 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
were logged, the log file would contain
### 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
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 ‘You have:’ and ‘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
You have: 90 deg - (5 deg + 22 min + 9 sec)
^
Illegal 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:
The log file would contain
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
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, units expands the alias in the log file.
The ‘From:’ and ‘To:’ tags are written to the log file even if the ‘--quiet’ option is
given. If the log file exists when 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 ‘--log’
option is ignored when units is used non-interactively.
INVOKING UNITS
You invoke units like this:
units [options] [from-unit [to-unit]]
If the from-unit and to-unit are omitted, the program will use interactive prompts to
determine which conversions to perform. See Interactive Use. If both from-unit and to-
unit are given, units will print the result of that single conversion and then exit. If
only from-unit appears on the command line, 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 ‘--quiet’
option is enabled by default if you specify from-unit on the command line. See Command
Line Use.
The default behavior of 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 ‘-’ followed by a
single character) or long form (‘--’ 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, ‘--out %f’ works, but ‘--o %f’ fails because units has other long options
beginning with ‘o’. However, ‘--q’ works because ‘--quiet’ is the only long option
beginning with ‘q’.
Some options require arguments to specify a value (e.g., ‘-d 12’ or ‘--digits 12’).
Short-form options that do not take arguments may be concatenated (e.g., ‘-erS’ is
equivalent to ‘-e -r -S’); the last option in such a list may be one that takes an
argument (e.g., ‘-ed 12’). With short-form options, the space between an option and its
argument is optional (e.g., ‘-d12’ is equivalent to ‘-d 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., ‘--output-format’ and
‘--exponential’) are given in combination, behavior is controlled by the last option
given. For example, ‘-o%.12f -e’ gives exponential format with the default eight
significant digits).
The following options are available:
-c, --check
Check that all units and prefixes defined in the units data file reduce to
primitive units. Print a list of all units that cannot be reduced. 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 units
with this option after modifying a units data file.
--check-verbose, --verbose-check
Like the ‘--check’ option, this option prints a list of units that cannot be
reduced. But to help find unit definitions that cause endless loops, it lists the
units as they are checked. If units hangs, then the last unit to be printed has a
bad definition. Only definitions active in the current locale are checked.
-d ndigits, --digits ndigits
Set the number of significant digits in the output to the value specified (which
must be greater than zero). For example, ‘-d 12’ sets the number of significant
digits to 12. With exponential output 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, units will print a warning and set the
number to the largest meaningful value. To directly set the maximum value, give an
argument of max (e.g., ‘-d max’). Be aware, of course, that “significant” here
refers only to the 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 ‘--digits’ option conflicts with the ‘--output-format’ option.
-e, --exponential
Set the numeric output format to exponential (i.e., scientific notation), like that
used in the Unix units program. The default precision is eight significant digits
(seven digits to the right of the decimal point); this can be changed with the
‘--digits’ option. The ‘--exponential’ option conflicts with the ‘--output-format’
option.
-o format, --output-format format
This option affords complete control over the numeric output format using the
specified format. The format is a single floating point numeric format for the
printf() function in the C programming language. All compilers support the format
types ‘g’ and ‘G’ to specify significant digits, ‘e’ and ‘E’ for scientific
notation, and ‘f’ for fixed-point decimal. The ISO C99 standard introduced the ‘F’
type for fixed-point decimal and the ‘a’ and ‘A’ types for hexadecimal floating
point; these types are allowed with compilers that support them. The default
format is ‘%.8g’; for greater precision, you could specify ‘-o %.15g’. See Numeric
Output Format and the documentation for printf() for more detailed descriptions of
the format specification. The ‘--output-format’ option affords the greatest
control of the output appearance, but requires at least rudimentary knowledge of
the printf() format syntax. If you don’t want to bother with the printf() syntax,
you can specify greater precision more simply with the ‘--digits’ option or select
exponential format with ‘--exponential’. The ‘--output-format’ option is
incompatible with the ‘--exponential’ and ‘--digits’ options.
-f filename, --file filename
Instruct units to load the units file filename. You can specify up to 25 units
files on the command line. When you use this option, units will load 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 filename is the empty
string (‘-f ""’), the default units file (or that specified by UNITSFILE) will be
loaded in addition to any others specified with ‘-f’.
-L logfile, --log logfile
Save the results of calculations in the file 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
logfile exits, the new results are appended to the file. This option is ignored
when units is used non-interactively. See Logging Calculations for a more detailed
description and some examples.
-H filename, --history filename
Instruct units to save history to filename, so that a record of your commands is
available for retrieval across different units invocations. To prevent the history
from being saved set filename to the empty string (‘-H ""’). This option has no
effect if readline is not available.
-h, --help
Print out a summary of the options for units.
-m, --minus
Causes ‘-’ to be interpreted as a subtraction operator. This is the default
behavior.
-p, --product
Causes ‘-’ 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: ‘(-3)’. By
default ‘-’ is treated as a subtraction operator.
--oldstar
Causes ‘*’ to have the old-style precedence, higher than the precedence of division
so that ‘1/2*3’ will equal ‘1/6’.
--newstar
Forces ‘*’ to have the new (default) precedence that follows the usual rules of
algebra: the precedence of ‘*’ is the same as the precedence of ‘/’, so that
‘1/2*3’ will equal ‘3/2’.
-r, --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.
-S, --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|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., ‘3|8 in’ rather than ‘3 * 1|8 in’). In some
cases, this is not what is wanted; for example, the results for a cooking recipe
might show ‘3 * 1|2 cup’ as ‘3|2 cup’. With the ‘--show-factor’ option, a result
equivalent to 1.5 cups will display as ‘3 * 1|2 cup’ rather than ‘3|2 cup’. A
user-specified fractional unit with a numerator other than 1 is never overridden,
however—if a unit list specifies ‘3|4 cup;1|2 cup’, a result equivalent to 1 1/2
cups will always be shown as ‘2 * 3|4 cup’ whether or not the ‘--show-factor’
option is given.
--conformable
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, units
will exit with an error message and return failure.
-v, --verbose
Give slightly more verbose output when converting units. When combined with the
‘-c’ option this gives the same effect as ‘--check-verbose’. When combined with
‘--version’ produces a more detailed output, equivalent to the ‘--info’ option.
-V, --version
Print the program version number, tell whether the readline library has been
included, tell whether UTF-8 support has been included; give the locale, the
location of the default 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 ‘--terse’ option, the program prints only the
version number and exits.
When given in combination with the ‘--verbose’ option, the program, the ‘--version’
option has the same effect as the ‘--info’ option below.
-I, --info
Print the information given with the ‘--version’ option, show the pathname of the
units program, show the status of the UNITSFILE and MYUNITSFILE environment
variables, and additional information about how units locates the related files.
On systems running Microsoft Windows, the status of the 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 ‘--version’ and ‘--verbose’ options has the same effect as giving
‘--info’.
-U, --unitsfile
Print the location of the default units data file and exit; if the file cannot be
found, print “Units data file not found”.
-u (gauss[ian]|esu|emu), --units (gauss[ian]|esu|emu)
Specify a CGS units system: Gaussian, ESU, or EMU.
-l locale, --locale locale
Force a specified locale such as ‘en_GB’ to get British definitions by default.
This overrides the locale determined from system settings or environment variables.
See Locale for a description of locale format.
-n, --nolists
Disable conversion to unit lists.
-s, --strict
Suppress conversion of units to their reciprocal units. For example, 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.
-1, --one-line
Give only one line of output (the forward conversion); do not print the reverse
conversion. If a reciprocal conversion is performed, then units will still print
the “reciprocal conversion” line.
-t, --terse
Print only a single conversion factor. This option can be used when calling units
from another program so that the output is easy to parse. This option has the
combined effect of these options: ‘--strict’ ‘--quiet’ ‘--one-line’ ‘--compact’.
When combined with ‘--version’ it produces a display showing only the program name
and version number.
--compact
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 ‘--verbose’ option.
-q, --quiet, --silent
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 units displays the results. This option is turned on by
default if you invoke units with a unit expression on the command line.
SCRIPTING WITH UNITS
Despite its numerous options, 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 ‘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 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:
#!/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
When units is invoked with no non-option arguments, it reads have/want pairs, on
alternating lines, from its standard input, so the task can be accomplished with only two
invocations of 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
conformable, running
$ conformable 3.75g | grep 0.120
gives
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
So we might conclude that the scale is calibrated in troy ounces.
We might run
$ units --verbose are
Definition: 100 m^2 = 100 m^2
and wonder if ‘are’ has any synonyms, value. To find out, we could run
$ conformable are | grep "= 1 "
are = 1 a
are = 1 are
OUTPUT STYLES
The output can be tweaked in various ways using command line options. With no options,
the output looks like this
$ units
Currency exchange rates from FloatRates (USD base) on 2019-02-20
3070 units, 109 prefixes, 109 nonlinear units
You have: 23ft
You want: m
* 7.0104
/ 0.14264521
You have: m
You want: ft;in
3 ft + 3.3700787 in
This is arguably a bit cryptic; the ‘--verbose’ option makes clear what the output means:
$ units --verbose
Currency exchange rates from FloatRates (USD base) on 2019-02-20
3070 units, 109 prefixes, 109 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
The ‘--quiet’ option suppresses the clutter displayed when units starts, as well as the
prompts to the user. This option is enabled by default when you give units on the command
line.
$ units --quiet
23 ft
m
* 7.0104
/ 0.14264521
$ units 23ft m
* 7.0104
/ 0.14264521
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:
$ 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
Note that when converting to a unit list, the ‘--compact’ option displays a semicolon
separated list of results. Also be aware that the ‘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 ‘--strict’ option, which suppresses reciprocal
conversions. Similarly you can suppress unit list conversion using ‘--nolists’. It is
impossible to prevent the three line error output.
$ units --compact --nolists m 'ft;in'
Error in 'ft;in': Parse error
$ units --one-line --strict 23ft 1/m
The various style options can be combined appropriately. The ultimate combination is the
‘--terse’ option, which combines ‘--strict’, ‘--quiet’, ‘--one-line’, and ‘--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 units and then process its result.
$ 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
ADDING YOUR OWN DEFINITIONS
Units Data Files
The units and prefixes that units can convert are defined in the units data file,
typically ‘/usr/share/units/definitions.units’. If you can’t find this file, run
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 units.
You can include additional data files in the units database using the ‘!include’ command
in the standard units data file. For example
!include /usr/local/share/units/local.units
might be appropriate for a site-wide supplemental data file. The location of the
‘!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 ‘!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 units -c after making changes to any units data file.
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 ‘.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 ‘unitdef.units’.) Running units -V will display the location and name of your
personal units file.
The units program first tries to determine your home directory from the HOME environment
variable. On systems running Microsoft Windows, if HOME does not exist, units attempts to
find your home directory from HOMEDRIVE, HOMEPATH and USERPROFILE. You can specify an
arbitrary file as your personal units data file with the 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 Data Files.
Defining New Units and Prefixes
A unit is specified on a single line by giving its name and an equivalence. Comments
start with a ‘#’ character, which can appear anywhere in a line. The backslash character
(‘\’) 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 ‘!include’ followed by the file’s name. The ‘!’ 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 ‘#’.
Unit names must not contain any of the operator characters ‘+’, ‘-’, ‘*’, ‘/’, ‘|’, ‘^’,
‘;’, ‘~’, the comment character ‘#’, or parentheses. They cannot begin or end with an
underscore (‘_’), a comma (‘,’) or a decimal point (‘.’). The figure dash (U+2012),
typographical minus ('-’; U+2212), and en dash ('--’; U+2013) are converted to the
operator ‘-’, so 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, the digit must be
preceded by a string beginning with an underscore, and afterwards consisting only of
digits, decimal points, or commas. For example, ‘foo_2’, ‘foo_2,1’, or ‘foo_3.14’ are
valid names but ‘foo2’ or ‘foo_a2’ are invalid. The underscore is necessary because
without it, units cannot determine whether ‘foo2’ is a unit name or represents ‘foo^2’.
Zero and one are exceptions because units never interprets them as exponents.
You could define nitrous oxide as
N2O nitrogen 2 + oxygen
but would need to define nitrogen dioxide as
NO_2 nitrogen + oxygen 2
Be careful to define new units in terms of old ones so that a reduction leads to the
primitive units, which are marked with ‘!’ characters. Dimensionless units are indicated
by using the string ‘!dimensionless’ for the unit definition.
When adding new units, be sure to use the ‘-c’ option to check that the new units reduce
properly. If you create a loop in the units definitions, then units will hang when
invoked with the ‘-c’ option. You will need to use the ‘--check-verbose’ option, which
prints out each unit as it is checked. The program will still hang, but the last unit
printed will be the unit that caused the infinite loop.
If you define any units that contain ‘+’ characters in their definitions, carefully check
them because the ‘-c’ option will not catch non-conformable sums. Be careful with the ‘-’
operator as well. When used as a binary operator, the ‘-’ character can perform addition
or multiplication depending on the options used to invoke units. To ensure consistent
behavior use ‘-’ only as a unary negation operator when writing units definitions. To
multiply two units leave a space or use the ‘*’ operator with care, recalling that it has
two possible precedence values and may require parentheses to ensure consistent behavior.
To compute the difference of ‘foo’ and ‘bar’ write ‘foo+(-bar)’ or even ‘foo+-bar’.
You may wish to intentionally redefine a unit. When you do this, and use the ‘-c’ option,
units displays a warning message about the redefinition. You can suppress these warnings
by redefining a unit using a ‘+’ at the beginning of the unit name. Do not include any
white space between the ‘+’ and the redefined unit name.
Here is an example of a short data file that defines some basic units:
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
A unit that ends with a ‘-’ character is a prefix. If a prefix definition contains any
‘/’ characters, be sure they are protected by parentheses. If you define ‘half- 1/2’,
then ‘halfmeter’ would be equivalent to ‘1 / (2 meter)’.
Defining Nonlinear Units
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 ‘inch 2.54 cm’ you are providing
information that 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:
tempF(x) units=[1;K] domain=[-459.67,) range=[0,) \
(x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32
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 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.
The definition begins with the unit name followed immediately (with no spaces) by a ‘(’
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 ‘units=[1;K]’ specification indicates that the ‘tempF’ function requires an
input argument conformable with ‘1’ (i.e., the argument is dimensionless), and that the
inverse function requires an input argument conformable with ‘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 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 ‘tempF’ function is
defined by
tempF(x) = (x+(-32)) degF + stdtemp
This gives a rule for converting ‘x’ in the units ‘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 ‘x(tempF)’ and its definition appears after a ‘;’ character. In our
example, the inverse is
x(tempF) = (tempF+(-stdtemp))/degF + 32
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 ‘;’ character
and the inverse definition, but then conversions to the unit will not be possible. If the
inverse definition is omitted, the ‘--check’ option will display a warning. It is up to
you to calculate and enter the correct inverse function to obtain proper conversions; the
‘--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
square(x) x^2
can have any arbitrary units, and can also take dimensionless arguments. In such a case,
you should 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,
squirt(x) sqrt(x)
is valid for a dimensionless argument, and for arguments with even powers of units.
Some definitions may not be valid for all real numbers. In such cases, units can handle
errors better if you specify an appropriate domain and range. You specify the domain and
range as shown below:
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
In this example the domain is specified after ‘domain=’ with the endpoints given in
brackets. 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 ‘(0,)’:
decibel(x) units=[1;1] range=(0,) 10^(x/10); 10 log(decibel)
If the domain or range is given, the second endpoint must be greater than the first.
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
‘units=[1;ft]’ and ‘range=[3,)’, the range will be taken as 3 ft to infinity. If the
function is passed a parameter of ‘900 mm’, that value will be adjusted to 2.9527559 ft,
which is outside the specified range. If you omit the units specification from the
previous example, units can not tell whether you intend the lower endpoint to be 3 ft or
3 microfurlongs, and can not adjust the parameter value of 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 units to perform better error checking and give
more helpful error messages. Giving the domain and range also enables the ‘--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 ‘~’ operator. So to create a
synonym for ‘tempF’ you could write
fahrenheit(x) units=[1;K] tempF(x); ~tempF(fahrenheit)
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,
dBW(x) units=[1;W] range=[0,) dB(x) W ; ~dB(dBW/W)
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
‘tempF’ you could write
fahrenheit() tempF
The definition must be a nonlinear unit; for example, the synonym
fahrenheit() meter
will result in an error message when units starts.
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 ‘units=’ specification. Specifying the
range as the nonnegative numbers can prevent cryptic error messages.
circlearea(r) units=[m;m^2] range=[0,) pi r^2 ; sqrt(circlearea/pi)
Defining 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
zincgauge[in] 1 0.002, 10 0.02, 15 0.04, 19 0.06, 23 0.1
In this example, ‘zincgauge’ is the name of the piecewise linear unit. The definition of
such a unit is indicated by the embedded ‘[’ character. After the bracket, you should
indicate the units to be attached to the numbers in the table. No spaces can appear
before the ‘]’ character, so a definition like ‘foo[kg meters]’ is invalid; instead write
‘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 ‘zincgauge’ at five points. For example, we set
‘zincgauge(1)’ equal to ‘0.002 in’. Definitions like this may be more readable if
written using continuation characters as
zincgauge[in] \
1 0.002 \
10 0.02 \
15 0.04 \
19 0.06 \
23 0.1
With the preceding definition, the following conversion can be performed:
You have: zincgauge(10)
You want: in
* 0.02
/ 50
You have: .01 inch
You want: zincgauge
5
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, units will return
the smallest inverse.
After adding nonlinear units definitions, you should normally run units --check to check
for errors. If the ‘units’ keyword is not given, the ‘--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,
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
Running 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:
ansicoated[micron] \
. . .
600 10.55 \
800 11.5 \
1000 9.5 \
Running units --check would give the error message
Table 'ansicoated' lacks unique inverse around entry 800
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 ‘noerror’ keyword; for the examples above, this could be done as
squirt(x) noerror domain=[0,) range=[0,) sqrt(x); squirt^2
ansicoated[micron] noerror \
. . .
Use the ‘noerror’ keyword with caution. The safest approach after adding a nonlinear unit
definition is to run units --check and confirm that there are no actual errors before
adding the ‘noerror’ keyword.
Defining Unit List Aliases
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 ‘!unitlist’ and includes the alias and the definition; for
example, the aliases included in the standard units data file are
!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
Unit list aliases are only for unit lists, so the definition must include a ‘;’. Unit
list aliases can never be combined with units or other unit list aliases, so the
definition of ‘time’ shown above could not have been shortened to ‘year;day;hms’.
As usual, be sure to run units --check to ensure that the units listed in unit list
aliases are conformable.
NUMERIC OUTPUT FORMAT
By default, units shows results to eight significant digits. You can change this with the
‘--exponential’, ‘--digits’, and ‘--output-format’ options. The first sets an exponential
format (i.e., scientific notation) like that used in the original Unix 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 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 ‘--digits’ and ‘--exponential’ options. The
‘--output-format’ option affords the greatest control of the output appearance, but
requires at least rudimentary knowledge of the printf() format syntax. See Invoking Units
for descriptions of these options.
Format Specification
The format specification recognized with the ‘--output-format’ option is a subset of that
for printf(). The format specification has the form %[flags][width][.precision]type; it
must begin with ‘%’, and must end with a floating-point type specifier: ‘g’ or ‘G’ to
specify the number of significant digits, ‘e’ or ‘E’ for scientific notation, and ‘f’ for
fixed-point decimal. The ISO C99 standard added the ‘F’ type for fixed-point decimal and
the ‘a’ and ‘A’ types for hexadecimal floating point; these types are allowed with
compilers that support them. Type length modifiers (e.g., ‘L’ to indicate a long double)
are inapplicable and are not allowed.
The default format for units is ‘%.8g’; for greater precision, you could specify
‘-o %.15g’. The ‘g’ and ‘G’ format types use exponential format whenever the exponent
would be less than -4, so the value 0.000013 displays as ‘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 5e7 displays as ‘50000000’ and the value 5e8 displays as
‘5e+008’. If you prefer fixed-point display, you might specify ‘-o %.8f’; however, small
numbers will display very few significant digits, and values less than 0.5e-8 will show
nothing but zeros.
The format specification may include one or more optional flags: ‘+’, ‘ ’ (space), ‘#’,
‘-’, or ‘0’ (the digit zero). The digit-grouping flag ‘'’ 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., ‘.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.
Flags
The ‘+’ flag causes the output to have a sign (‘+’ or ‘-’). The space flag ‘ ’ is similar
to the ‘+’ 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 ‘+’ flag is also given. The ‘+’ or
‘ ’ flag could be useful if conversions might include positive and negative results, and
you wanted to align the decimal points in exponential notation. The ‘#’ 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 ‘g’ or ‘G’ types, the ‘#’ flag also prevents the suppression of trailing
zeros. The digit-grouping flag ‘'’ shows a thousands separator in digits to the left of
the decimal point. This can be useful when displaying large numbers in fixed-point
decimal; for example, with the format ‘%f’,
You have: mile
You want: microfurlong
* 8000000.000000
/ 0.000000
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 (‘,’),
the output with the format ‘%'f’ might be
You have: mile
You want: microfurlong
* 8,000,000.000000
/ 0.000000
making the magnitude readily apparent. Unfortunately, few compilers support the digit-
grouping flag.
With the ‘-’ 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 ‘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 ‘%011.6f’,
You have: troypound
You want: grain
* 5760.000000
/ 0000.000174
The ‘0’ flag has no effect if the ‘-’ (left align) flag is given.
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 units than with long columnar output, but it may nonetheless assist in quickly
assessing the relative magnitudes of results. For example, with the format ‘%12.6f’,
You have: km
You want: in
* 39370.078740
/ 0.000025
You have: km
You want: rod
* 198.838782
/ 0.005029
You have: km
You want: furlong
* 4.970970
/ 0.201168
Precision
The meaning of “precision” depends on the format type. With ‘g’ or ‘G’, it specifies the
number of significant digits (like the ‘--digits’ option); with ‘e’, ‘E’, ‘f’, or ‘F’, it
specifies the maximum number of digits to be shown after the decimal point.
With the ‘g’ and ‘G’ format types, trailing zeros are suppressed, so the results may
sometimes have fewer digits than the specified precision (as indicated above, the ‘#’ flag
causes trailing zeros to be displayed).
The default precision is 6, so ‘%g’ is equivalent to ‘%.6g’, and would show the output to
six significant digits. Similarly, ‘%e’ or ‘%f’ would show the output with six digits
after the decimal point.
The C 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 units is
15 decimal digits (or 13 hexadecimal digits). With the ‘--digits’ option, you are limited
to the maximum internal precision; with the ‘--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 ‘%.18g’, the output might be
You have: pound
You want: grain
* 6999.9999999999991
/ 0.00014285714285714287
With the format ‘%.25g’ you might get the following:
You have: 1/3
You want:
Definition: 0.333333333333333314829616256247
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. The
precision affects only the 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 printf() for more detailed descriptions of the format
specification.
The ‘--output-format’ option is incompatible with the ‘--exponential’ or ‘--digits’
options; if the former is given in combination with either of the latter, the format is
controlled by the last option given.
LOCALIZATION
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.
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 units
program attempts to determine the locale from the POSIX setlocale function; if this cannot
be done, units examines the environment variables LC_CTYPE and LANG. On POSIX systems, a
locale is of the form language_country, where language is the two-character code from ISO
639-1 and country is the two-character code from ISO 3166-1; language is lower case and
country is upper case. For example, the POSIX locale for the United Kingdom is en_GB.
On systems running Microsoft Windows, the value returned by setlocale() is different from
that on POSIX systems; units attempts to map the Windows value to a POSIX value by means
of a table in the 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 ‘locale_map.txt’ file comprises two tab-
separated columns; each entry is of the form
Windows-locale POSIX-locale
where POSIX-locale is as described above, and Windows-locale typically spells out both the
language and country. For example, the entry for the United States is
English_United States en_US
You can force units to run in a desired locale by using the ‘-l’ option.
In order to create unit definitions for a particular locale you begin a block of
definitions in a unit datafile with ‘!locale’ followed by a locale name. The ‘!’ must be
the first character on the line. The units program reads the following definitions only
if the current locale matches. You end the block of localized units with ‘!endlocale’.
Here is an example, which defines the British gallon.
!locale en_GB
gallon 4.54609 liter
!endlocale
Additional Localization
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, 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 ‘!var’ or
‘!varnot’ following by an environment variable name and then a space separated list of
values. The leading ‘!’ must appear in the first column of a units data file, and the
conditional block is terminated by ‘!endvar’. Definitions in blocks beginning with ‘!var’
are executed only if the environment variable is exactly equal to one of the listed
values. Definitions in blocks beginning with ‘!varnot’ are executed only if the
environment variable does 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 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:
!var INCH_UNIT usa
yard 3600|3937 m
!endvar
!var INCH_UNIT canada
yard 0.9144 meter
!endvar
!var INCH_UNIT uk
yard 0.91439841 meter
!endvar
!var INCH_UNIT canada uk usa
foot 1|3 yard
inch 1|12 foot
!endvar
!var INCH_UNIT france
foot 144|443.296 m
inch 1|12 foot
line 1|12 inch
!endvar
!varnot INCH_UNIT usa uk france canada
!message Unknown value for INCH_UNIT
!endvar
When units reads the above definitions it will check the environment variable INCH_UNIT
and load only the definitions for the appropriate section. If INCH_UNIT is unset or is
not set to one of the four values listed, then units will run the last block. In this
case that block uses the ‘!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 ‘!set’ command, which sets an environment variable only if it is not already set;
these settings are only for the current units invocation and do not persist. So if the
example above were preceded by ‘!set INCH_UNIT france’, then this would make ‘france’ the
default value for INCH_UNIT. If the user had set the variable in the environment before
invoking units, then units would use the user’s value.
To link these settings to the user’s locale you combine the ‘!set’ command with the
‘!locale’ command. If you wanted to combine the above example with suitable locales you
could do by preceding the above definition with the following:
!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
These definitions set the overall default for INCH_UNIT to ‘france’ and set default values
for four locales appropriately. The overall default setting comes last so that it only
applies when INCH_UNIT was not set by one of the other commands or by the user.
If the variable given after ‘!var’ or ‘!varnot’ is undefined, then units prints an error
message and ignores the definitions that follow. Use ‘!set’ to create defaults to prevent
this situation from arising. The ‘-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.
ENVIRONMENT VARIABLES
The units program uses the following environment variables:
HOME Specifies the location of your home directory; it is used by units to find a
personal units data file ‘.units’. On systems running Microsoft Windows, the file
is ‘unitdef.units’, and if HOME does not exist, units tries to determine your home
directory from the HOMEDRIVE and HOMEPATH environment variables; if these variables
do not exist, units finally tries USERPROFILE—typically ‘C:\Users\username’
(Windows Vista and Windows 7) or ‘C:\Documents and Settings\username’ (Windows XP).
LC_CTYPE, LANG
Checked to determine the locale if units cannot obtain it from the operating
system. Sections of the standard units data file are specific to certain locales.
MYUNITSFILE
Specifies your personal units data file. If this variable exists, units uses its
value rather than searching your home directory for ‘.units’. The personal units
file will not be loaded if any data files are given using the ‘-f’ option.
PAGER 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 ‘+n’n syntax
for specifying a line number. The default pager is more; PAGER can be used to
specify alternatives such as less, pg, emacs, or vi.
UNITS_ENGLISH
Set to either ‘US’ or ‘GB’ to choose United States or British volume definitions,
overriding the default from your locale.
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 ‘-f’ option, the file specified by UNITSFILE will be not
be loaded unless the ‘-f’ option is given with the empty string (‘units -f ""’).
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 ‘-f’ option or the
UNITSFILE environment variable, and that location does not also contain the locale
map file.
UNITS_SYSTEM
This environment variable is used in the standard data file to select CGS
measurement systems. Currently supported systems are ‘esu’, ‘emu’, ‘gauss[ian]’,
and ‘si’. The default is ‘si’.
DATA FILES
The units program uses two default data files: ‘definitions.units’ and ‘currency.units’.
The program can also use an optional personal units data file ‘.units’ (‘unitdef.units’
under Windows) located in the user’s home directory. The personal units data file is
described in more detail in Units Data Files.
On Unix-like systems, the data files are typically located in ‘/usr/share/units’ if units
is provided with the operating system, or in ‘/usr/local/share/units’ if units is compiled
from the source distribution. Note that the currency 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., ‘C:/usr/local’), and
units is compiled from the source distribution. If Unix-like commands are not available,
a more common location is ‘C:\Program Files (x86)\GNU\units’ (for 64-bit Windows
installations) or ‘C:\Program Files\GNU\units’ (for 32-bit installations).
If units is obtained from the GNU Win32 Project (http://gnuwin32.sourceforge.net/), the
files are commonly in ‘C:\Program Files\GnuWin32\share\units’.
If the default units data file is not an absolute pathname, units will look for the file
in the directory that contains the units program; if the file is not found there, units
will look in a directory ../share/units relative to the directory with the units program.
You can determine the location of the files by running units --version. Running
units --info will give you additional information about the files, how units will attempt
to find them, and the status of the related environment variables.
UNICODE SUPPORT
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 ‘!utf8’ and ending with ‘!endutf8’.
The non-ASCII definitions are loaded only if the platform and the locale support UTF-8.
Platform support is determined when units is compiled; the locale is checked at every
invocation of units. To see if your version of units includes Unicode support, invoke the
program with the ‘--version’ option.
When Unicode support is available, 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,
units ignores the entire line. In addition to checking validity, 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 ‘search’ and ‘?’ commands.
As of early 2019, Microsoft Windows provides limited support for UTF-8 in console
applications, and accordingly, units does not support Unicode 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 ‘!utf8’ ...
‘!endutf8’ to ensure that they are only loaded when Unicode support is available. As
usual, the ‘!’ must appear as the first character on the line. As discussed in Units Data
Files, it’s usually best to put such definitions in supplemental data files linked by an
‘!include’ command or in a personal units data file.
When Unicode support is not available, 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 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 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 outside ‘!utf8’
Typeset material other than code examples usually uses the Unicode minus (U+2212) rather
than the ASCII hyphen-minus operator (U+002D) used in units; the figure dash (U+2012) and
en dash (U+2013) are also occasionally used. To allow such material to be copied and
pasted for interactive use or in units data files, units converts these characters to
U+002D before further processing. Because of this, none of these characters can appear in
unit names.
READLINE SUPPORT
If the readline package has been compiled in, then when units is used interactively,
numerous command line editing features are available. To check if your version of units
includes readline, invoke the program with the ‘--version’ option.
For complete information about readline, consult the documentation for the readline
package. Without any configuration, units will allow editing in the style of emacs. Of
particular use with units are the completion commands.
If you type a few characters and then hit ESC followed by ?, then units will display a
list of all the units that start with the characters typed. For example, if you type metr
and then request completion, you will see something like this:
You have: metr
metre metriccup metrichorsepower metrictenth
metretes metricfifth metricounce metricton
metriccarat metricgrain metricquart metricyarncount
You have: metr
If there is a unique way to complete a unit name, you can hit the TAB key and units will
provide the rest of the unit name. If units beeps, it means that there is no unique
completion. Pressing the 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
‘.units_history’ in your home directory so that it will persist across multiple units
invocations. If you wish to keep work for a certain project separate you can change the
history filename using the ‘--history’ option. You could, for example, make an alias for
units to units --history .units_history so that 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 units each one will save its new history to
the history file upon exit.
UPDATING CURRENCY EXCHANGE RATES
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 units
cannot provide real-time values. To update the exchange rates, run units_cur, which
rewrites the file containing the currency rates, typically ‘/var/lib/units/currency.units’
or ‘/usr/local/com/units/currency.units’ on a Unix-like system or
‘C:Program Files (x86)\:GNU\:units\:definitions.units’ on a Windows system.
This program requires Python (https://www.python.org); either version 2 or 3 will work.
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:
• FloatRates (https://www/floatrates.com). The US dollar (‘USD’) is the default base
currency. You can change the base currency with the ‘-b’ option described below.
Allowable base currencies are listed on the FloatRates website. Exchange rates update
daily.
• The European Central Bank (https://www.ecb.europa.eu). The base currency is always
the euro (‘EUR’). Exchange rates update daily. This source offers a more limited
list of currencies than the others.
• Fixer (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.
• open exchange rates (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.
The default source is FloatRates; you can select a different one using ‘-s’ option
described below.
Precious metals pricing is obtained from Packetizer (www.packetizer.com). This site
updates once per day.
You invoke units_cur like this:
units_cur [options] [outfile]
By default, the output is written to the default currency file described above; this is
usually what you want, because this is where units looks for the file. If you wish, you
can specify a different filename on the command line and units_cur will write the data to
that file. If you give ‘-’ for the file it will write to standard output.
The following options are available:
-h, --help
Print a summary of the options for units_cur.
-V, --version
Print the units_cur version number.
-v, --verbose
Give slightly more verbose output when attempting to update currency exchange
rates.
-s source, --source source
Specify the source for currency exchange rates; currently supported values are
‘floatrates’ (for FloatRates), ‘eubank’ (for the European Central Bank), ‘fixer’
(for Fixer), and ‘openexchangerates’ (for open exchange rates); the last two
require an API key to be given with the ‘-k’ option.
-b base, --base base
Set the base currency (when allowed by the site providing the data). base should
be a 3-letter ISO currency code, e.g., ‘USD’. The specified currency will be the
primitive currency unit used by 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 Enter at the ‘You want:’ prompt. This option is
ignored if the source does not allow specifying the base currency. (Currently only
floatrates supports this option.)
-k key, --key key
Set the API key to key for sources that require it.
DATABASE COMMAND SYNTAX
unit definition
Define a regular unit.
prefix- definition
Define a prefix.
funcname(var) noerror units=[in-units,out-units] domain=[x1,x2] range=[y1,y2]
definition(var) ; inverse(funcname)
Define a nonlinear unit or unit function. The four optional keywords noerror,
units=, range= and domain= can appear in any order. The definition of the inverse
is optional.
tabname[out-units] noerror pair-list
Define a piecewise linear unit. The pair list gives the points on the table listed
in ascending order. The noerror keyword is optional.
!endlocale
End a block of definitions beginning with ‘!locale’
!endutf8
End a block of definitions begun with ‘!utf8’
!endvar
End a block of definitions begun with ‘!var’ or ‘!varnot’
!include file
Include the specified file.
!locale value
Load the following definitions only of the locale is set to value.
!message text
Display text when the database is read unless the quiet option (‘-q’) is enabled.
If you omit text, then units will display a blank line. Messages will also appear
in the log file.
!prompt text
Prefix the ‘You have:’ prompt with the specified text. If you omit text, then any
existing prefix is canceled.
!set variable value
Sets the environment variable, variable, to the specified value only if it is not
already set.
!unitlist alias definition
Define a unit list alias.
!utf8 Load the following definitions only if units is running with UTF-8 enabled.
!var envar value-list
Load the block of definitions that follows only if the environment variable envar
is set to one of the values listed in the space-separated value list. If envar is
not set, units prints an error message and ignores the block of definitions.
!varnot envar value-list
Load the block of definitions that follows only if the environment variable envar
is set to value that is not listed in the space-separated value list. If envar is
not set, units prints an error message and ignores the block of definitions.
FILES
/usr/share/units/definitions.units — the standard units data file
AUTHOR
units was written by Adrian Mariano
12 November 2020 UNITS(1)