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Unless agreed otherwise, units should conform with the recommendations of the IAU Style Manual (McNally [1988]). Unfortunately, this manual defines units as they would appear in a published document rather than as they must appear in plain character form. George & Angelini ([1995]) and Ochsenbein et al. ([1996]) have prepared detailed documents on this subject upon which the following remarks are based. In particular, the following tables are taken from George & Angelini's manuscript (with some changes and additions). Readers should consult these references for examples and expanded discussion. We allow the possibility that the interpretation of CUNITia may depend on conventions established for the CTYPEia associated with them. For example, units specified by "s" might mean SI seconds or seconds of sidereal time.

The basic units string, called str1 and str2 in Table 3, is composed of a unit string taken from Col. 2 of the IAU-recognized units in Table 5 or the extended astronomical units in Table 6. All units from the former and selected units from the latter may be preceded, with no intervening blanks by a single character (two for deca) taken from Table 4 and representing scale factors mostly in steps of 103. Compound prefixes (e.g., ZYeV for 1045 eV) are prohibited. A compound string may then be created from these simple strings by one of the notations in Table 3. A unit raised to a power is indicated by the unit string followed, with no intervening blanks, by the optional symbols ** or - followed by the power given as a numeric expression, called expr in Table 3. The power may be a simple integer, with or without sign, optionally surrounded by parentheses. It may also be a decimal number (e.g., 1.5, .5) or a ratio of two integers (e.g. 7/9), with or without sign, which are always surrounded by parentheses. Thus meters squared is indicated by m**(2), m**+2, m+2, m2, m-2, m-(+2), etc. and per meter cubed is indicated by m**-3, m-3, m-(-3), /m3, and so forth. Meters to the three halves may be indicated by m(1.5), m-(1.5), m**(1.5), m(3/2), m**(3/2), and m-(3/2), but not by m-3/2 or m1.5.

Table 3. Characters & strings allowed to denote mathematical operations.

String Meaning

str1 str2 Multiplication
str1*str2 Multiplication
str1.str2 Multiplication
str1/str2 Division
str1**expr Raised to the power expr
str1^expr Raised to the power expr
str1expr Raised to the power expr
log(str1) Common Logarithm (to base 10)
ln(str1) Natural Logarithm
exp(str1) Exponential (estr1)
sqrt(str1) Square root

Table 4. Prefixes for multiples & submultiples.

Submult Prefix Char Mult Prefix Char

10-1 deci d 10 deca da
10-2 centi c 102 hecto h
10-3 milli m 103 kilo k
10-6 micro u 106 mega M
10-9 nano n 109 giga G
10-12 pico p 1012 tera T
10-15 femto f 1015 peta P
10-18 atto a 1018 exa E
10-21 zepto z 1021 zetta Z
10-24 yocto y 1024 yotta Y

Table 5. IAU-recommended basic units.

Quantity Unit Meaning Notes

SI base & supplementary units
length m meter
mass kg kilogram g gram okay
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
IAU-recognized derived units
frequency Hz hertz s-1
energy J joule N m
power W watt J s-1
electric potential V volt J C-1
force N newton kg m s-2
pressure, stress Pa pascal N m-2
electric charge C coulomb A s
electric resistance Ohm ohm V A-1
electric conductance S siemens A V-1
electric capacitance F farad C V-1
magnetic flux Wb weber V s
magnetic flux density T tesla Wb m-2
inductance H henry Wb A-1
luminous flux lm lumen cd sr
illuminance lx lux lm m-2

Note that functions such as log actually require dimensionless arguments, so, by log(Hz), for example, we actually mean log(x/1Hz). The final string to be given as the value of CUNITia is the compound string, or a compound of compounds, preceded by an optional numeric multiplier of the form 10**k, 10^k, or 10±k where k is an integer, optionally surrounded by parentheses with the sign character required in the third form in the absence of parentheses. FITS writers are encouraged to use the numeric multiplier only when the available standard scale factors of Table 4 will not suffice. Parentheses are used for symbol grouping and are strongly recommended whenever the order of operations might be subject to misinterpretation. A blank character implies multiplication which can also be conveyed explicitly with an asterisk or a period. Therefore, although blanks are allowed as symbol separators, their use is discouraged. Two examples are '10**(46)erg/s' and 'sqrt(erg/pixel/s/GHz)'. Note that case is significant throughout. The IAU style manual forbids the use of more than one solidus (/) character in a units string. In the present conventions, normal mathematical precedence rules are assumed to apply, and we, therefore, allow more than one solidus. However, authors might wish to consider, for example, 'sqrt(erg/(pixel.s.GHz))' instead of the form given previously.

Table 6. Additional allowed units.

Quantity Unit Meaning Notes

plane angle deg degree of arc /180 rad
arcmin minute of arc 1/60 deg
arcsec second of arc 1/3600 deg
mas milli-second of arc 1/3600000 deg
time min minute
h hour
d day 86400 s
a year (Julian) 31557600 s (365.25 d), peta a (Pa) forbidden
yr year (Julian) a is IAU-style
energy* eV electron volt 1.6021765×10-19 J
erg erg 10-7 J
Ry rydberg 1/2 (2pie2 / hc)2 mec2 = 13.605692 eV
mass* solMass solar mass 1.9891×1030 kg
u unified atomic mass unit 1.6605387×10-27 kg
luminosity solLum Solar luminosity 3.8268×1026 W
length Angstrom angstrom 10-10 m
solRad Solar radius 6.9599×108 m
AU astronomical unit 1.49598×1011 m
lyr light year 9.460730×1015 m
pc parsec 3.0857×1016 m
events count count
ct count
photon photon
ph photon
flux density Jy jansky 10-26 W m-2 Hz-1
mag (stellar) magnitude
R rayleigh 1010 / (4pi) photons m-2 s-1 sr-1
magnetic field †‡ G gauss 10-4 T
area pixel (image/detector) pixel
pix (image/detector) pixel
†‡ barn barn 10-28 m2
Miscellaneous "units"
D debye 1/3 ×10-29 C.m
Sun relative to Sun e.g. abundances
chan (detector) channel
bin numerous applications (including the 1-d analogue of pixel)
voxel 3-d analogue of pixel
bit binary information unit
byte (computer) byte 8 bit
adu Analog-to-digital converter
beam beam area of observation as in Jy/beam

† - addition of prefixes for decimal multiples and submultiples are allowed.
‡ - deprecated in IAU Style Manual (McNally [1988]) but still in use.
* - conversion factors from CODATA Internationally recommended values of the fundamental physical constants 1998 (

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