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 IAUrecognized 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 10^{3}. Compound prefixes (e.g., ZYeV
for
10^{45} 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
,
m3
,
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
.
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 (e^{str1}) 
sqrt(str1) 
Square root 
Submult  Prefix  Char  Mult  Prefix  Char 
10^{1}  deci  d 
10  deca  da 
10^{2}  centi  c 
10^{2}  hecto  h 
10^{3}  milli  m 
10^{3}  kilo  k 
10^{6}  micro  u 
10^{6}  mega  M 
10^{9}  nano  n 
10^{9}  giga  G 
10^{12}  pico  p 
10^{12}  tera  T 
10^{15}  femto  f 
10^{15}  peta  P 
10^{18}  atto  a 
10^{18}  exa  E 
10^{21}  zepto  z 
10^{21}  zetta  Z 
10^{24}  yocto  y 
10^{24}  yotta  Y 
Quantity  Unit  Meaning  Notes 
String  
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  
IAUrecognized 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.
Quantity  Unit  Meaning  Notes  
String  
plane angle  deg 
degree of arc  /180 rad  
arcmin 
minute of arc  1/60 deg  
arcsec 
second of arc  1/3600 deg  
mas 
millisecond 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 IAUstyle 

energy^{*}  †  eV 
electron volt  1.6021765×10^{19} J 
‡  erg 
erg  10^{7} J  
Ry 
rydberg  1/2 (2e^{2} / hc)^{2} m_{e}c^{2} = 13.605692 eV  
mass^{*}  solMass 
solar mass  1.9891×10^{30} kg  
u 
unified atomic mass unit  1.6605387×10^{27} kg  
luminosity  solLum 
Solar luminosity  3.8268×10^{26} W  
length  ‡  Angstrom 
angstrom  10^{10} m 
solRad 
Solar radius  6.9599×10^{8} m  
AU 
astronomical unit  1.49598×10^{11} m  
lyr 
light year  9.460730×10^{15} m  
†  pc 
parsec  3.0857×10^{16} 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  10^{10} / (4) 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} m^{2}  
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 1d analogue of pixel)  
voxel 
3d analogue of pixel  
†  bit 
binary information unit  
†  byte 
(computer) byte  8 bit  
adu 
Analogtodigital 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 (http://physics.nist.gov/cuu/Constants/) 