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UNITS(1) UNITS(1)
NAME
units - unit conversion program
OVERVIEW OF `UNITS'
The `units' program converts quantities expressed in vari-
ous scales to their equivalents in other scales. The
`units' program can handle multiplicative scale changes as
well as nonlinear conversions such as Fahrenheit to Cel-
sius.
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 use the program interactively with prompts, or you
can use it from the command line.
INTERACTING WITH `UNITS'
To invoke units for interactive use, type `units' at your
shell prompt. The program will print something like this:
2131 units, 53 prefixes, 24 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 type
of units you want to convert to. To convert to feet, you
would type `feet'.
The answer will be displayed in two ways. The first line
of output, which is marked with a `*' to indicate multi-
plication, 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 .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 .03048 dekameters. But the number given the
other direction is inexact.
If you try to 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 which measure
reciprocal dimensions, then `units' will display the con-
version results with an extra note indicating that recip-
rocal 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 return 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.
If you want a list of options you can type `?' at the `You
want:' prompt. The program will display a list of named
units which are conformable with the unit that you entered
at the `You have:' prompt above. Note that conformable
unit combinations will not appear on this list.
Typing `help' at either prompt displays a short help mes-
sage. 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 defi-
nition and comments that may give more details or histori-
cal information about the unit.
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 units expression, and type the
new units you want. You will probably need to protect the
units expressions from interpretation by the shell using
single 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 (0) to the calling environment. If `units' is
given non-conformable units to convert, it will print a
message giving the reduced form of each unit and it will
return failure (nonzero) to the calling environment.
When `units' is invoked 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 EXPRESSIONS
In order to enter more complicated units or fractions, you
will need to use operations such as powers, products and
division. Powers of units can be specified using the `^'
character as shown in the following example, or by simple
concatenation: `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. The `^'
operator has the second highest precedence.
You have: cm^3
You want: gallons
* 0.00026417205
/ 3785.4118
You have: arabicfoot-arabictradepound-force
You want: ft lbf
* 0.7296
/ 1.370614
Multiplication of units can be specified by using spaces,
a hyphen (`-') or an asterisk (`*'). Division of units is
indicated by the slash (`/') or by `per'.
You have: furlongs per fortnight
You want: m/s
* 0.00016630986
/ 6012.8727
Multiplication has a higher precedence than division and
is evaluated left to right, so `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 recip-
rocal length equivalent to .5/meter, which is probably not
what you would intend if you entered that expression. You
can indicate division of numbers with the vertical dash
(`|'). This operator has the highest precedence so the
square root of two thirds could be written `2|3^1|2'.
You have: 1|2 inch
You want: cm
* 1.27
/ 0.78740157
Parentheses can be used for grouping as desired.
You have: (1/2) kg / (kg/meter)
You want: league
* 0.00010356166
/ 9656.0833
Prefixes are defined separately from base units. In order
to get centimeters, the units database defines `centi-'
and `c-' as prefixes. Prefixes can appear alone with no
unit following them. An exponent applies only to the
immediately preceding unit and its prefix so that `cm^3'
or `centimeter^3' refer to cubic centimeters but `centi-
meter^3' refers to hundredths of cubic meters. Only one
prefix is permitted per unit, so `micromicrofarad' will
fail, but `micro-microfarad' will work.
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
which 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
dollars^5.
Outside of the SI system, it is often desirable to add
values of different units together. Sums of conformable
units are written 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 which are added together must reduce to
identical expressions in primitive units, or an error mes-
sage will be displayed:
You have: 12 printerspoint + 4 heredium
^
Illegal sum of non-conformable units
Because `-' is used for products, it cannot also be used
to form differences of units. If a `-' appears after `('
or after `+' then it will act as a negation operator. So
you can compute 20 degrees minus 12 minutes by entering
`20 degrees + -12 arcmin'. The `+' character is sometimes
used in exponents like `3.43e+8'. This leads to an ambi-
guity in an expression like `3e+2 yC'. The unit `e' is a
small unit of charge, so this can be regarded as equiva-
lent to `(3e+2) yC' or `(3 e)+(2 yC)'. This ambiguity is
resolved by always interpreting `+' as part of an exponent
if possible.
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 dimen-
sions 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. Higher roots can be
obtained 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
Nonlinear units are represented using functional notation.
They make possible nonlinear unit conversions such temper-
ature. This is different from the linear units that con-
vert temperature differences. Note the difference below.
The absolute temperature conversions are handled by units
starting with `temp', and you must use functional nota-
tion. The temperature differences 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
In this case, think of `tempF(x)' not as a function but as
a notation which indicates that `x' should have units of
`tempF' attached to it. @xref{Nonlinear units}.
Some other examples of nonlinears units are ring size and
wire gauge. There are numerous different gauges and ring
sizes. See the units database for more details. Note
that 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 units database.
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
INVOKING `UNITS'
You invoke `units' like this:
units OPTIONS [FROM-UNIT [TO-UNIT]]
If the FROM-UNIT and TO-UNIT are omitted, then the program
will use interactive prompts to determine which conver-
sions to perform. If both FROM-UNIT and TO-UNIT are
given, `units' will print the result of that single con-
version 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 will
need to be quoted to protect them from shell interpreta-
tion and to group them into two arguments. @xref{Command
line use}.
The following options allow you to read in an alternative
units file, check your units file, or change the output
format:
-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. Note that only
definitions active in the current locale are
checked.
--check-verbose
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. Note that only definitions active in
the current locale are checked.
-o format, --output-format format
Use the specified format for numeric output. For-
mat is the same as that for the printf function in
the ANSI C standard. For example, if you want more
precision you might use `-o %.15g'.
-f filename, --file filename
Use filename as the units data file rather than the
default units data file. This option overrides the
`UNITSFILE' environment variable.
-h, --help
Print out a summary of the options for `units'.
-q, --quiet, --silent
Suppress prompting of the user for units and the
display of statistics about the number of units
loaded.
-s, --strict
Suppress conversion of units to their reciprocal
units.
-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.
UNIT DEFINITIONS
The conversion information is read from a units data file
which is called `units.dat' and is probably located in the
`/usr/local/share' 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 permitivity of vacuum
G gravitational constant
mach speed of sound
The database includes atomic masses for all of the ele-
ments 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 unit `pound' is a unit of mass. To get force, multi-
ply by the force conversion unit `force' or use the short-
hand `lbf'. (Note that `g' is already taken as the stan-
dard 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
counterparts, such as the British Imperial gallon, are
prefixed with `br'. Currency is prefixed with its country
name: `belgiumfranc', `britainpound'.
The US Survey foot, yard, and mile can be obtained by
using the `US' prefix. These units differ slightly from
the international length units. They were in general use
until 1959, and are still used for geographic surveys.
The acre is officially defined in terms of the US Survey
foot. If you want an acre defined according to the inter-
national foot, use `intacre'. The difference between
these units is about 4 parts per million. The British
also used a slightly different length measure before 1959.
These can be obtained with the prefix `UK'.
When searching for a unit, if the specified string does
not appear exactly as a unit name, then the `units' pro-
gram will try to remove a trailing `s' or a trailing `es'.
If that fails, `units' will check for a prefix. All of
the standard metric prefixes are defined.
To find out what units and prefixes are available, read
the standard units data file.
DEFINING NEW UNITS
All of the units and prefixes that `units' can convert are
defined in the units data file. If you want to add your
own units, you can supply your own file.
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 char-
acter (`') 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.
Unit names must not contain any of the operator characters
`+', `-', `*', `/', `|', `^' or the parentheses. They
cannot begin with a digit or a decimal point (`.'), nor
can they end with a digit (except for zero). 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
`!' characters. When adding new units, be sure to use the
`-c' option to check that the new units reduce properly.
If you define any units which contain `+' characters,
carefully check them because the `-c' option will not
catch non-conformable sums. If you create a loop in the
units definitions, then `units' will hang when invoked
with the `-c' options. You will need to use the `--check-
verbose' option which prints out each unit as it checks
them. The program will still hang, but the last unit
printed will be the unit which caused the infinite loop.
Here is an example of a short units file that defines some
basic units:
m ! # The meter is a primitive unit
sec ! # The second is a 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 which 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 units conversions of interest are nonlinear; for
example, temperature conversions between the Fahrenheit
and Celsius scales cannot be done by simply multiplying by
conversions 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 nota-
tion. It is best to regard this notation not as a func-
tion call but as a way of adding units to a number, much
the same way that writing a linear unit name after a num-
ber adds units to that number. Internally, nonlinear
units are defined by a pair of functions which convert to
and from linear units in the data file, so that an even-
tual conversion to primitive units is possible.
Here is an example nonlinear unit definition:
tempF(x) [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 specify
the dimensions.
The definition begins with the unit name followed immedi-
ately (with no spaces) by a `(' character. In parentheses
is the name of the parameter. Next is an optional speci-
fication of the units required by the functions in this
definition. In the example above, the `tempF' function
requires an input argument conformable with `1'. For nor-
mal nonlinear units definitions the forward function will
always take a dimensionless argument. The inverse func-
tion requires an input argument conformable with `K'. In
general the inverse function will need units that match
the quantity measured by your nonlinear unit. The sole
purpose of the expression in brackets to enable `units' to
perform error checking on function arguments.
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 tempera-
ture. The inverse can be omitted by leaving out the `;'
character, but then conversions to the unit will be impos-
sible. If the inverse is omitted then the `--check'
option will display a warning. It is up to you to calcu-
late and enter the correct inverse function to obtain
proper conversions. The `--check' option tests the
inverse at one point and print 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 func-
tions. Inverse functions can be obtained using the `~'
operator. So to create a synonym for `tempF' you could
write
fahrenheit(x) [1;K] tempF(x); ~tempF(fahrenheit)
You may occasionally wish to define a function that oper-
ates 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. Note
that this definition requires a length as input and pro-
duces an area as output, as indicated by the specification
in brackets.
circlearea(r) [m;m^2] 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 `[' 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 illegal; instead
write `foo[kg*meters]'. The definition of the unit con-
sists 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 spec-
ified in brackets). In this example, we define `zinc-
gauge' 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 preceeding 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. The `--check' option will
print a warning if a non-monotonic piecewise linear unit
is encountered.
LOCALIZATION
Some units have different values in different locations.
The localization feature accomodates this by allowing the
units database to specify region dependent definitions.
A locale region in the units database begins with
`!locale' followed by the name of the locale. The leading
`!' must appear in the first column of the units database.
The locale region is terminated by `!endlocale'. The fol-
lowing example shows how to define a couple units in a
locale.
!locale en_GB
ton brton
gallon brgallon
!endlocale
The current locale is specified by the `LOCALE' environ-
ment variable. Note that the `-c' option only checks the
definitions which are active for the current locale.
ENVIRONMENT VARIABLES
The `units' programs uses the following environment vari-
ables.
LOCALE Specifies the locale. The default is `en_US'.
Sections of the units database are specific to cer-
tain locales.
PAGER Specifies the pager to use for help and for dis-
playing the conformable units. The help function
browses the units database and calls the pager
using the `+nn' syntax for specifying a line num-
ber. The default pager is `more', but `less',
`emacs', or `vi' are possible alternatives.
UNITSFILE
Specifies the units database file to use (instead
of the default). This will be overridden by the
`-f' option.
READLINE SUPPORT
If the `readline' package has been compiled in, then when
`units' is used interactively, numerous command line edit-
ing features are available. To check if your version of
`units' includes the readline, invoke the program with the
`--version' option.
For complete information about readline, consult the docu-
mentation for the readline package. Without any configu-
ration, `units' will allow editing in the style of emacs.
Of particular use with `units' are the completion com-
mands.
If you type a few characters and then hit `ESC' followed
by the `?' key then `units' will display a list of all the
units which 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 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.
FILES
/usr/local/share/units.dat - the standard units data file
AUTHOR
Adrian Mariano (adrian@cam.cornell.edu)
30 Jan 2001 UNITS(1)