The adopted syntax is that described in FITS-WCS paper I "Representation of World Coordinate in FITS" by Greisen & Calabretta. We distinguish here between “basic” units and “derived” units: derived units are defined in terms of other units (either derived or basic), whereas basic units have no such definitions. Derived units may be represented by their own symbol (e.g. “Jy”—the Jansky) or by a mathematical expression which combines other symbols and constants to form a definition of the unit (e.g. “km/s”—kilometres per second). Unit symbols may be prefixed by a string representing a standard multiple or sub-multiple.
In addition to the unit symbols listed in FITS-WCS Paper I, any other arbitrary unit symbol may be used, with the proviso that it will not be possible to convert between Frames using such units. The exception to this is if both Frames refer to the same unknown unit string. For instance, an axis with unknown unit symbol "flop" could be converted to an axis with unit "Mflop" (Mega-flop).
Unit symbols (optionally prefixed with a multiple or sub-multiple) can be combined together using a limited range of mathematical operators and functions, to produce new units. Such expressions may also contain parentheses and numerical constants (these may optionally use “scientific” notation including an “E” character to represent the power of 10).
The following tables list the symbols for the basic and derived units which may be included in a units string, the standard prefixes for multiples and sub-multiples, and the strings which may be used to represent mathematical operators and functions.
Basic units | ||
Quantity | Symbol | FullFull Name |
length | m | metre |
mass | g | gram |
time | s | second |
plane angle | rad | radian |
solid angle | sr | steradian |
temperature | K | Kelvin |
electric current | A | Ampere |
amount of substance | mol | mole |
luminous intensity | cd | candela |
Derived units | |||
Quantity | Symbol | Full Name | Definition |
area | barn | barn | 1.0E-28 m**2 |
area | pix | pixel | |
area | pixel | pixel | |
electric capacitance | F | Farad | C/V |
electric charge | C | Coulomb | A s |
electric conductance | S | Siemens | A/V |
electric potential | V | Volt | J/C |
electric resistance | Ohm | Ohm | V/A |
energy | J | Joule | N m |
energy | Ry | Rydberg | 13.605692 eV |
energy | eV | electron-Volt | 1.60217733E-19 J |
energy | erg | erg | 1.0E-7 J |
events | count | count | |
events | ct | count | |
events | ph | photon | |
events | photon | photon | |
flux density | Jy | Jansky | 1.0E-26 W /m**2 /Hz |
flux density | R | Rayleigh | 1.0E10/(4*PI) photon.m**-2 /s/sr |
flux density | mag | magnitude | |
force | N | Newton | kg m/s**2 |
frequency | Hz | Hertz | 1/s |
illuminance | lx | lux | lm/m**2 |
inductance | H | Henry | Wb/A |
length | AU | astronomical unit | 1.49598E11 m |
length | Angstrom | Angstrom | 1.0E-10 m |
length | lyr | light year | 9.460730E15 m |
length | pc | parsec | 3.0867E16 m |
length | solRad | solar radius | 6.9599E8 m |
luminosity | solLum | solar luminosity | 3.8268E26 W |
luminous flux | lm | lumen | cd sr |
magnetic field | G | Gauss | 1.0E-4 T |
magnetic flux | Wb | Weber | V s |
mass | solMass | solar mass | 1.9891E30 kg |
mass | u | unified atomic mass unit | 1.6605387E-27 kg |
magnetic flux density | T | Tesla | Wb/m**2 |
plane angle | arcmin | arc-minute | 1/60 deg |
plane angle | arcsec | arc-second | 1/3600 deg |
plane angle | mas | milli-arcsecond | 1/3600000 deg |
plane angle | deg | degree | pi/180 rad |
power | W | Watt | J/s |
pressure, stress | Pa | Pascal | N/m**2 |
time | a | year | 31557600 s |
time | d | day | 86400 s |
time | h | hour | 3600 s |
time | yr | year | 31557600 s |
time | min | minute | 60 s |
D | Debye | 1.0E-29/3 C.m |
Prefixes for multiples & sub-multiples | |||||
Sub-multiple | Name | Prefix | Sub-multiple | Name | Prefix |
deci | d | deca | da | ||
centi | c | hecto | h | ||
milli | m | kilo | k | ||
micro | u | mega | M | ||
nano | n | giga | G | ||
pico | p | tera | T | ||
femto | f | peta | P | ||
atto | a | exa | E | ||
zepto | z | zetta | Z | ||
yocto | y | yotta | Y |
Mathematical operators & functions | |
String | Meaning |
sym1 sym2 | multiplication (a space) |
sym1*sym2 | multiplication (an asterisk) |
sym1.sym2 | multiplication (a dot) |
sym1/sym2 | division |
sym1**y | exponentiation ( |
sym1^ y |
exponentiation ( |
log(sym1) | common logarithm |
ln(sym1) | natural logarithm |
exp(sym1) | exponential |
sqrt(sym1) | square root |