Standards for Astronomical Catalogues, Version 2.0 (pdf)(February 2000)

3.2  Standard of Catalogues: Units

The unit in which physical parameters are expressed is a fundamental parameter which becomes especially important when data are to be compared, or used outside a specialized field of science — most physicists have never heard of astronomy-specific units.

Special care has been taken to try to use the standard SI units, and to convert if necessary the unit to such standards: for instance, we use the string 0.1nm to express Angströms (Å=10–10m), since the Angström is a non-standard unit. Another example is mW/m2 , the milliwatt per m2, which is identical to the CGS erg/cm2/s unit, which is not used outside our discipline.

Only simple power functions of physical units are accepted, which means that e.g. solMass3/2 (solar mass at a 3/2 power) cannot be a valid unit. Some values are however traditionnally written in a decimal logarithmic scale, and we introduced bracketed units like [solMass] to indicate logM unit, i.e. a value representing solar masses expressed on a logarithmic scale.

The standard adopted here differs from the OGIP ones ( OGIP memo 93-001 about ``Specification of Physical Units within OGIP FITS files" by Ian M. George & Lorella Angelini, August 1993) for the syntax of composite units (operator symbols), and in the usage of math functions (only the square bracketted units, representing the log function is accepted here) and of obsolete CGS units which are not avoided here; the basic symbols however agree.

3.2.1  Syntax of Units

The syntax of the unit expression is summarized by the following rules:

Rule 1: any unit is described by a single word — no space is allowed. For instance, the Angström is coded 0.1nm, and never 0.1 nm; the kilometer-per-second is coded km/s, or km.s-1, but never km / s or km s-1.

Rule 2: the only allowed numerical factor is at the very beginning of the Unit string. The structure of the unit is therefore the concatenation of factor and unit_expression and we will write the ``number of pixels per Å" as 10pix/nm, and neither pix/0.1nm nor pix/(0.1nm).

The numerical factor may include the letter x for the multiplication, as 1.5x10+11 to express the number 1.5×1011

Rule 3: The operators to express a compound unit are

/ for the division — as in km/s . for the multiplication (the dot is however understood as a decimal point in the leading numerical factor) — as in kW.h nothing for a power — as m2 for m2 or 10+21 for 1021.
Note that + or signs are not operators, but represent the leading sign of numeric values.

Rule 4: a simple (non-compound) unit is made of a basic unit symbol, eventually preceded by a multiple prefix.

Among several possible expressions of a unit, it is preferable to choose the shortest one; this leads also to prefer the division (/) to the multiplication of the inverse, e.g. prefer km/s to km.s-1.

3.2.2  Basic symbols

Basic Unit Symbols

Symbol Explanation Definition
(c) Unitless value (c) % Unitless value, in percent 10–2 (a) a year (also yr) 365.25d = 31.5576×106s (b) A Ampere (a) AU astronomical unit 1.49598×1011m (a) arcmin minute of arc 1/60 ° (a) arcsec second of arc 1/60 arcmin (e) barn barn (cross-section) 10–28 m2 (c) bit binary information unit (computer storage) (c) byte byte (computer storage) 8 bit C Coulomb (electric charge) As (b) cd Candela (luminous intensity) (c) ct Count (events) D Debye (1/3)×10–29 Cm (a) d day 24h = 86.4×103s (a) deg degree of arc (°) π/180 rad (e) eV electron-Volt 1.602177×10–19 J F Farad (electric capacitance) C/V (b) g gram 10–3 kg (a) h hour of time (sideral if appropriate) 3600s H Henry (inductance) Wb/A Hz Hertz (frequency) s–1 J Joule (energy) Nm (a) Jy Jansky 10–26 W/m2/Hz (b) K Kelvin lm lumen (luminous flux) cdsr lx lux (illuminance) lm/m2 (b) m metre (a) mag magnitudes (a) mas millisecond of arc (π/6.48)×10–8 rad (a) min minute of time (sideral if appropriate) (b) mol mole N Newton (force) kgm/s2 Ohm (Ω) Ohm (electric resistance) V/A Pa Pascal (pressure) N/m2 (a) pc parsec 3.0857 ×1016m (c) pix pixel (image element) (b) rad radian (angle) (e) Ry Rydberg (energy) (1/2) (2πe2/hc)2mec2 = 13.60583 eV (b) s second of time S Siemens (electric conductance) A/V (c) solLum Solar luminosity 3.826×1026 W (c) solMass Solar mass 1.989×1030 kg (c) solRad Solar radius 6.9599×108 m (c) Sun Unit referring to the Sun (e.g. abundances) sr steradian (solid angle) T Tesla (magnetic field intensity) Wb/m2 V Volts (electric potential) W/A W Watt (power) J/s Wb Weber (magnetic flux) Vs (c) yr year (also a) 365.25d = 31.5576×106s
The basic symbols listed include basic standard SI units (b), the extensions listed by the IAU style book marked (a), other frequent physical extensions (e), and a few further extensions used at CDS (c).

3.2.3  Multiples

Symbols used to express multiples and submultiples

Symbol Explanation Value
d deci 10–1 c centi 10–2 m milli 10–3 u micro (µ) 10–6 n nano 10–9 p pico 10–12 f femto 10–15 a atto 10–18 z zepto 10–21 y yocto 10–24

Symbol Explanation Value
da deca 10 h hecto 102 k kilo 103 M mega 106 G giga 109 T tera 1012 P peta 1015 E exa 1018 Z zetta 1021 Y yotta 1024
The standard SI multiple and submultiple prefixes can be used; these are summarized in multiple. Note that a single prefix can only be attached to a unit symbol, which means that e.g. mmas must not be used to designate a µ-arc-second, but rather uarcsec.

See the Unit Calculator