calc: Predefined Units
12.3 Predefined Units
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The definitions of many units have changed over the years. For example,
the meter was originally defined in 1791 as one ten-millionth of the
distance from the Equator to the North Pole. In order to be more
precise, the definition was adjusted several times, and now a meter is
defined as the distance that light will travel in a vacuum in
1/299792458 of a second; consequently, the speed of light in a vacuum is
exactly 299792458 m/s. Many other units have been redefined in terms of
fundamental physical processes; a second, for example, is currently
defined as 9192631770 periods of a certain radiation related to the
cesium-133 atom. The only SI unit that is not based on a fundamental
physical process (although there are efforts to change this) is the
kilogram, which was originally defined as the mass of one liter of
water, but is now defined as the mass of the international prototype of
the kilogram (IPK), a cylinder of platinum-iridium kept at the Bureau
international des poids et mesures in Sèvres, France. (There are
several copies of the IPK throughout the world.) The British imperial
units, once defined in terms of physical objects, were redefined in 1963
in terms of SI units. The US customary units, which were the same as
British units until the British imperial system was created in 1824,
were also defined in terms of the SI units in 1893. Because of these
redefinitions, conversions between metric, British Imperial, and US
customary units can often be done precisely.
Since the exact definitions of many kinds of units have evolved over
the years, and since certain countries sometimes have local differences
in their definitions, it is a good idea to examine Calc’s definition of
a unit before depending on its exact value. For example, there are
three different units for gallons, corresponding to the US (‘gal’),
Canadian (‘galC’), and British (‘galUK’) definitions. Also, note that
‘oz’ is a standard ounce of mass, ‘ozt’ is a Troy ounce, and ‘ozfl’ is a
fluid ounce.
The temperature units corresponding to degrees Kelvin and Centigrade
(Celsius) are the same in this table, since most units commands treat
temperatures as being relative. The ‘calc-convert-temperature’ command
has special rules for handling the different absolute magnitudes of the
various temperature scales.
The unit of volume “liters” can be referred to by either the
lower-case ‘l’ or the upper-case ‘L’.
The unit ‘A’ stands for amperes; the name ‘Ang’ is used for
angstroms.
The unit ‘pt’ stands for pints; the name ‘point’ stands for a
typographical point, defined by ‘72 point = 1 in’. This is slightly
different than the point defined by the American Typefounder’s
Association in 1886, but the point used by Calc has become standard
largely due to its use by the PostScript page description language.
There is also ‘texpt’, which stands for a printer’s point as defined by
the TeX typesetting system: ‘72.27 texpt = 1 in’. Other units used by
TeX are available; they are ‘texpc’ (a pica), ‘texbp’ (a “big point”,
equal to a standard point which is larger than the point used by TeX),
‘texdd’ (a Didot point), ‘texcc’ (a Cicero) and ‘texsp’ (a scaled TeX
point, all dimensions representable in TeX are multiples of this value).
When Calc is using the TeX or LaTeX language mode (
TeX and
LaTeX Language Modes), the TeX specific unit names will not use the
‘tex’ prefix; the unit name for a TeX point will be ‘pt’ instead of
‘texpt’, for example. To avoid conflicts, the unit names for pint and
parsec will simply be ‘pint’ and ‘parsec’ instead of ‘pt’ and ‘pc’.
The unit ‘e’ stands for the elementary (electron) unit of charge;
because algebra command could mistake this for the special constant ‘e’,
Calc provides the alternate unit name ‘ech’ which is preferable to ‘e’.
The name ‘g’ stands for one gram of mass; there is also ‘gf’, one
gram of force. (Likewise for ‘lb’, pounds, and ‘lbf’.) Meanwhile, one
“‘g’” of acceleration is denoted ‘ga’.
The unit ‘ton’ is a U.S. ton of ‘2000 lb’, and ‘t’ is a metric ton of
‘1000 kg’.
The names ‘s’ (or ‘sec’) and ‘min’ refer to units of time; ‘arcsec’
and ‘arcmin’ are units of angle.
Some “units” are really physical constants; for example, ‘c’
represents the speed of light, and ‘h’ represents Planck’s constant.
You can use these just like other units: converting ‘.5 c’ to ‘m/s’
expresses one-half the speed of light in meters per second. You can
also use this merely as a handy reference; the ‘u g’ command gets the
definition of one of these constants in its normal terms, and ‘u b’
expresses the definition in base units.
Two units, ‘pi’ and ‘alpha’ (the fine structure constant,
approximately 1/137) are dimensionless. The units simplification
commands simply treat these names as equivalent to their corresponding
values. However you can, for example, use ‘u c’ to convert a pure
number into multiples of the fine structure constant, or ‘u b’ to
convert this back into a pure number. (When ‘u c’ prompts for the “old
units,” just enter a blank line to signify that the value really is
unitless.)
Info Catalog
calc: The Units Table
calc: Units
calc: User-Defined Units