UNITS(1) UNITS(1)
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NAME
units - unit conversion and calculation program
SYNOPSIS
'units' [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 the examples below. The program can also perform
conversions from and to sums of units, such as converting between
meters and feet plus inches.
Beyond simple unit conversions, 'units' can be used as a general-
purpose scientific calculator that keeps track of units in its calcu-
lations. 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 con-
sistency when working with long expressions that involve many dif-
ferent units that may combine in complex ways.
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.
Basic operation is simple: you enter the units that you want to con-
vert 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.
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 04/23/12
2516 units, 85 prefixes, 65 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 the
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tab key can be used to complete unit names. See Readline Support for
more information about 'readline'. To quit the program press Ctrl-C
or Ctrl-D under Unix. Under Windows press Ctrl-Z.
The answer 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 out-
put, 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 obvi-
ous 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
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Reciprocal conversion can be suppressed by using the '--strict'
option. As usual, use the '--verbose' option to get more comprehensi-
ble 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 combina-
tion 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
Named dimensionless units are not treated as dimensionless in other
contexts. They cannot be used as exponents so for example,
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'meter^radian' is not allowed.
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 con-
formable 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 histor-
ical 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 origi-
nal unit expression, and type the new units you want. If a units
expression contains non-alphanumeric characters, you may need to pro-
tect 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.
If the conversion is successful, then '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 environ-
ment.
When you invoke 'units' with only one argument, it will print out 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
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'/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 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'. British capacity units that differ from their US counter-
parts, such as the British Imperial gallon, are prefixed with 'br'.
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 per-
mitted 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.
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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 Interna-
tional 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
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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 opera-
tions such as powers, multiplication, division, 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 prior-
ity multiplication using a space, and a high priority numerical
division operator ('|') that can simplify some expressions.
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. An exponent like '2^3^2' is evaluated
right to left as usual. The '^' operator has the second highest pre-
cedence. You can also use '**' as an exponent operator.
You have: cm^3
You want: gallons
* 0.00026417205
/ 3785.4118
You have: arabicfoot * arabictradepound * force
You want: ft lbf
* 0.7296
/ 1.370614
You multiply units using a space or an asterisk ('*'). The example
above shows both forms. You can divide units using the slash ('/') or
with 'per'.
You have: furlongs per fortnight
You want: m/s
* 0.00016630986
/ 6012.8727
When a unit includes a prefix, exponent operators apply to the combi-
nation, so 'centimeter^3' gives cubic centimeters. If you separate
the prefix from the unit with any multiplication operator, such as
'centi meter^3', then the prefix is treated as a separate unit, so the
exponent does not apply. The second example would be a hundredth of a
cubic meter, not a centimeter.
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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: 'W / m^2 Hz'. If you multiply with '*' then you must
group the terms in the denominator with parentheses: 'W / (m^2 * Hz)'.
The higher precedence of the space operator may not always be advanta-
geous. 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 '*' operator is
convenient for multiplying a sequence of quotients. With the '*'
operator, the example above becomes 'm/s * s/day', which is equivalent
to 'm/day'. Similarly, you could write '1/2 * meter' to get half a
meter. Alternatively, parentheses can be used for grouping: you could
write '(1/2) meter' to get half a meter. See Complicated Unit Expres-
sions for an illustration of the various options.
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'. This operator
has the highest precedence, so you can write the square root of two
thirds '2|3^1|2'. You cannot use the vertical bar to indicate divi-
sion of non-numerical units (e.g., 'm|s' results in an error message).
You have: 1|2 inch
You want: cm
* 1.27
/ 0.78740157
You can use parentheses for grouping:
You have: (1/2) kg / (kg/meter)
You want: league
* 0.00010356166
/ 9656.0833
Sums and Differences of Units
You may sometimes want to add values of different units that are out-
side 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
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* 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
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 multiplica-
tion 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
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/ 0.072
And the second example shows how the dollar sign in the units conver-
sion 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', 'ln',
'log', 'log2', 'exp', 'acos', 'atan' and 'asin'. 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.
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
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
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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 pre-
cedence than division using the slash. This differs from the usual
precedence rules, which give multiplication and division equal pre-
cedence, and can be confusing for people who think of units as a cal-
culator.
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
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several other ways to obtain unit products, and because '-' is a sub-
traction operator in general algebraic expressions, 'units' treats the
binary '-' as a subtraction operator by default. For backwards compa-
tibility use the '--product' option, which causes 'units' to treat the
binary '-' operator as a product operator. When '-' is a multiplica-
tion 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. Regard-
less 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 can-
not know what options will be in force when your definition is pro-
cessed.
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 conver-
sions 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 Non-
linear 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
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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 con-
verting to a temperature rather than converting a temperature incre-
ment.
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
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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 cir-
cleinch. 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
UNIT LISTS: CONVERSION TO SUMS OF
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 conver-
sion 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
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In converting to a sum of units like miles, feet and inches, you typi-
cally 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 coeffi-
cient 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)
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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 conform-
able with the You have unit that you enter.
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 disagree-
ment 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
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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 cal-
culations, 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.
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;
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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.
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
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 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
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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
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 defin-
ition 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. 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 char-
acters 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
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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 defini-
tion. 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 exponen-
tial 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 max-
imum, '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 preci-
sion, 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 for-
mat using the specified format. The format is a single floating
point numeric format for the 'printf()' function in the C pro-
gramming 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 '--
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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 speci-
fied with '-f'.
-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 sub-
traction operator.
--oldstar
Causes '*' to have the old-style precedence, higher than the pre-
cedence 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'.
--compact
Give compact output featuring only the conversion factor. This
turns off the '--verbose' option.
-q, --quiet, --silent
Suppress prompting of the user for units and the display of
statistics about the number of units loaded.
-n, --nolists
Disable conversion to unit lists.
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-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 exam-
ple, 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.
-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 conver-
sion, 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 per-
formed then 'units' will still print the ``reciprocal conver-
sion'' line.
-t, --terse
Give terse output when converting units. 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'.
-v, --verbose
Give slightly more verbose output when converting units. When
combined with the '-c' option this gives the same effect as '--
check-verbose'.
-V, --version
Print program version number, tell whether the 'readline' library
has been included, and give the location of the default units
data file.
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-l locale, --locale locale
Force a specified locale such as 'en_GB' to get British defini-
tions by default. This overrides the locale determined from sys-
tem settings or environment variables. See Locale for a descrip-
tion of locale format.
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'.
Although you can extend or modify this data file if you have appropri-
ate user privileges, it's usually better to put extensions in separate
files so that the definitions will be preserved when 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 defini-
tions 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 stan-
dard 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'.)
The 'units' program first tries to determine your home directory from
the 'HOME' environment variable. On systems running Microsoft Win-
dows, if 'HOME' does not exist, 'units' attempts to find your home
directory from 'HOMEDRIVE' and 'HOMEPATH'. Running 'units -V' will
display the location and name of your personal units file.
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.
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
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anywhere in a line. The backslash character ('\') acts as a continua-
tion 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 can-
not contain 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), typo-
graphical 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, 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'
would be valid names but 'foo2' or 'foo_a2' would be invalid. 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 reduc-
tion leads to the primitive units, which are marked with '!' charac-
ters. 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, 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 opera-
tor, the '-' character can perform addition or multiplication depend-
ing 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'.
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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 0.0254 m # Inch defined in terms of meters
ft 12 inches # The foot defined in terms of inches
mile 5280 ft # And the mile
A unit that ends with a '-' character is a prefix. If a prefix defin-
ition 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, tempera-
ture 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 func-
tional 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 data file, so that an eventual conversion to prim-
itive units is possible.
Here is an example nonlinear unit definition:
tempF(x) units=[1;K] (x+(-32)) degF + stdtemp ; \
(tempF+(-stdtemp))/degF + 32
A nonlinear unit definition comprises a unit name, a dummy parameter
name, two functions, and two corresponding units. The functions tell
'units' how to convert to and from the new unit. In order to produce
valid results, the arguments of these functions need to have the
correct dimensions. To facilitate error checking, you may optionally
indicate units for these arguments.
The definition begins with the unit name followed immediately (with no
spaces) by a '(' character. In parentheses is the name of the parame-
ter. Next is an optional specification of the units required by the
functions in this definition. In the example above, the 'tempF'
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function requires an input argument conformable with '1'. For normal
nonlinear units definitions the forward function will always take a
dimensionless argument. The inverse function requires an input argu-
ment conformable with 'K'. In general the inverse function will need
units that match the quantity measured by your nonlinear unit. The
purpose of the expression in brackets to enable 'units' to perform
error checking on function arguments, and also to assign units to
range and domain 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.
In order to make conversions to Fahrenheit possible, 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, but then conversions to the
unit will be impossible. If the inverse is omitted then 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.
If you wish to make synonyms for nonlinear units, you still need to
define 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)
You may define a function whose range and domain do not cover all of
the real numbers. In this case 'units' can handle errors better if
you specify an appropriate range and domain. You specify the range
and domain 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
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In this example the domain is specified after the 'domain=' with the
endpoints given in brackets. One of the end points can be omitted to
get an interval that goes to infinity. So the range could be speci-
fied as nonnegative by writing 'range=[0,]'. Both the range and
domain are optional and can appear independently and in any order
along with the 'units' specification. The values in the range and
domain are attached to the units given in the 'units' specification.
If you don't specify the units then the parameter inputs are reduced
to primitive units for the numeric comparison to the values you give
in the range or domain. In this case you should only use 'range' or
'domain' if the endpoints are zero and infinity.
Specifying the range and domain allows 'units' to perform better error
checking and give more helpful error messages when you invoke non-
linear units conversions outside of their bounds. It also enables the
'-c' option to find a point in the domain to use for its point check
of your inverse definition.
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. Specify-
ing 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)
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 '[' charac-
ter. After the bracket, you should indicate the units to be attached
to the numbers in the table. No spaces can appear before the ']' char-
acter, so a definition like 'foo[kg meters]' is illegal; 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 char-
acters as
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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 per-
formed:
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.
The '--check' option will print a warning if a non-monotonic piecewise
linear unit is encountered.
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., scien-
tific notation) like that used in the original Unix 'units' program,
the second allows you to specify a different number of significant
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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 exponen-
tial 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 fol-
lowed 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
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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 speci-
fied 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 colum-
nar 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
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* 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 preci-
sion (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 mean-
ingful. 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
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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 locali-
zation 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 for-
matting 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 setlo-
cale() 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' in the same directory, typically
'/usr/local/share/units', as the default units data files. The file
includes entries for many combinations of language and country, and
can be extended to include other combinations. The 'locale.map'
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.
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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 vari-
ables can be controled 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 defin-
itions 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
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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.
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If the variable given after '!var' or '!varnot' is undefined then
'units' prints an error message and ignores the definitions that fol-
low. 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, 'units' tries to determine your home
directory from the 'HOMEDRIVE' and 'HOMEPATH' environment vari-
ables if 'HOME' does not exist.
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 con-
formable 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 environ-
ment 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 ""').
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
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blocks beginning with '!utf8' and ending with '!endutf8'.
When 'units' starts, it checks the locale to determine the character
set. If 'units' is compiled with Unicode support and if the character
set is UTF-8, 'units' reads the UTF-8 definitions; otherwise these
definitions are ignored. When Unicode support is active, 'units' will
check every line of 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.
At present, 'units' does not support Unicode under Microsoft Windows.
The UTF-16 and UTF-32 encodings are not supported on any systems.
If definitions that contain non-ASCII 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 active, 'units' makes no assumptions about
character encoding, except that characters in the range 00-7F hexade-
cimal 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 char-
acters 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). 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
active, you should place any definitions with non-ASCII characters
outside '!utf8' ... '!endutf8' blocks-otherwise, they will be
ignored.
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 avail-
able. To check if your version of 'units' includes 'readline', invoke
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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 char-
acters typed. For example, if you type 'metr' and then request com-
pletion, 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 unitname, 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.
UPDATING CURRENCY EXCHANGE RATES
The units program includes currency exchange rates and prices for some
precious metals in the database. Of course, these values change over
time, sometimes very rapidly, and 'units' cannot provide real time
values. To update the exchange rates run the 'units_cur', which
rewrites the files containing the currency rates, typically
'/usr/local/share/units/currency.units'. This program must be run
with suitable permissions to write the file. To keep the rates
updated automatically, it could be run by a cron job on a Unix-like
system, or a similar scheduling program on a different system.
Currency exchange rates are taken from Time Genie
(http://www.timegenie.com) and precious metals pricing from Packetizer
(www.packetizer.com). These sites update once per day, so there is no
benefit in running the update script more often than daily. You can
run 'units_cur' with a filename specified on the command line and it
will write the data to that file. If you give '-' for the file it
will write to standard output.
DATABASE COMMAND SYNTAX
unit definition
Define a regular unit.
prefix- definition
Define a prefix.
definition(var) ; inverse(funcname)
funcname(var) units=[in-units,out-units] domain=[x1,x2] range=[y1,y2]
Define a nonlinear unit or unit function. The three optional
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keywords 'units=', 'range=' and 'domain=' can appear in any
order. The definition of the inverse is optional.
tabname[out-units] pair-list
Define a piecewise linear unit. The pair list gives the points
on the table listed in ascending order.
!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.
!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 variable value-list
Load the following definitions only if the environment variable,
variable is set to one of the values listed on the space
separated value list. If variable is not set then 'units' prints
an error message and ignores the following definitions.
!varnot variable value-list
Load the following definitions only if the environment variable,
variable is not set to one of the values listed on the space
separated value list. If variable is not set then 'units' prints
an error message and ignores the following definitions.
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GNU FREE DOCUMENTATION LICENSE
FILES
@DATAFILE@ - the standard units data file
AUTHOR
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