Standard Units

Standard units are defined in the astropy.units package as object instances.

All units are defined in terms of basic “irreducible” units. The irreducible units include:

  • Length (meter)

  • Time (second)

  • Mass (kilogram)

  • Current (ampere)

  • Temperature (Kelvin)

  • Angular distance (radian)

  • Solid angle (steradian)

  • Luminous intensity (candela)

  • Stellar magnitude (mag)

  • Amount of substance (mole)

  • Photon count (photon)

(There are also some more obscure base units required by the FITS Standard that are no longer recommended for use.)

Units that involve combinations of fundamental units are instances of CompositeUnit. In most cases, you do not need to worry about the various kinds of unit classes unless you want to design a more complex case.

There are many units already predefined in the module. You may use the find_equivalent_units() method to list all of the existing predefined units of a given type:

>>> from astropy import units as u
>>> u.g.find_equivalent_units()
  Primary name | Unit definition | Aliases
[
  M_e          | 9.10938e-31 kg  |                                  ,
  M_p          | 1.67262e-27 kg  |                                  ,
  earthMass    | 5.97217e+24 kg  | M_earth, Mearth                  ,
  g            | 0.001 kg        | gram                             ,
  jupiterMass  | 1.89812e+27 kg  | M_jup, Mjup, M_jupiter, Mjupiter ,
  kg           | irreducible     | kilogram                         ,
  solMass      | 1.98841e+30 kg  | M_sun, Msun                      ,
  t            | 1000 kg         | tonne                            ,
  u            | 1.66054e-27 kg  | Da, Dalton                       ,
]

Prefixes

Most units can be used with prefixes, with both the standard SI prefixes and the IEEE 1514-2002 binary prefixes (for bit and byte) supported:

Available decimal prefixes

Symbol

Prefix

Value

Q

quetta-

1e30

R

ronna-

1e27

Y

yotta-

1e24

Z

zetta-

1e21

E

exa-

1e18

P

peta-

1e15

T

tera-

1e12

G

giga-

1e9

M

mega-

1e6

k

kilo-

1e3

h

hecto-

1e2

da

deka-, deca

1e1

d

deci-

1e-1

c

centi-

1e-2

m

milli-

1e-3

u

micro-

1e-6

n

nano-

1e-9

p

pico-

1e-12

f

femto-

1e-15

a

atto-

1e-18

z

zepto-

1e-21

y

yocto-

1e-24

r

ronto-

1e-27

q

quecto-

1e-30

Available binary prefixes

Symbol

Prefix

Value

Ki

kibi-

2 ** 10

Mi

mebi-

2 ** 20

Gi

gibi-

2 ** 30

Ti

tebi-

2 ** 40

Pi

pebi-

2 ** 50

Ei

exbi-

2 ** 60

The Dimensionless Unit

In addition to these units, astropy.units includes the concept of the dimensionless unit, used to indicate quantities that do not have a physical dimension. This is distinct in concept from a unit that is equal to None: that indicates that no unit was specified in the data or by the user.

For convenience, there is a unit that is both dimensionless and unscaled: the dimensionless_unscaled object:

>>> u.dimensionless_unscaled
Unit(dimensionless)

Dimensionless quantities are often defined as products or ratios of quantities that are not dimensionless, but whose dimensions cancel out when their powers are multiplied.

Examples

To use the dimensionless_unscaled object:

>>> u.m / u.m
Unit(dimensionless)

For compatibility with the String Representations of Units and Quantities, this is equivalent to Unit('') and Unit(1), though using u.dimensionless_unscaled in Python code is preferred for readability:

>>> u.dimensionless_unscaled == u.Unit('')
True
>>> u.dimensionless_unscaled == u.Unit(1)
True

Note that in many cases, a dimensionless unit may also have a scale. For example:

>>> (u.km / u.m).decompose()
Unit(dimensionless with a scale of 1000.0)
>>> (u.km / u.m).decompose() == u.dimensionless_unscaled
False

As an example of why you might want to create a scaled dimensionless quantity, say you will be doing many calculations with some big unit-less number, big_unitless_num = 20000000  # 20 million, but you want all of your answers to be in multiples of a million. This can be done by dividing big_unitless_num by 1e6, but this requires you to remember that this scaling factor has been applied, which may be difficult to do after many calculations. Instead, create a scaled dimensionless quantity by multiplying a value by Unit(scale) to keep track of the scaling factor. For example:

>>> scale = 1e6
>>> big_unitless_num = 20 * u.Unit(scale)  # 20 million

>>> some_measurement = 5.0 * u.cm
>>> some_measurement * big_unitless_num  
<Quantity 100. 1e+06 cm>

To determine if a unit is dimensionless (but regardless of the scale), use the physical_type property:

>>> (u.km / u.m).physical_type
PhysicalType('dimensionless')
>>> # This also has a scale, so it is not the same as u.dimensionless_unscaled
>>> (u.km / u.m) == u.dimensionless_unscaled
False
>>> # However, (u.m / u.m) has a scale of 1.0, so it is the same
>>> (u.m / u.m) == u.dimensionless_unscaled
True

Enabling Other Units

By default, only the “default” units are searched by find_equivalent_units() and similar methods that do searching. This includes SI, CGS, and astrophysical units. However, you may wish to enable the Imperial or other user-defined units.

Example

To enable Imperial units, do:

>>> from astropy.units import imperial
>>> imperial.enable()
<astropy.units.core._UnitContext object at ...>
>>> u.m.find_equivalent_units()
  Primary name | Unit definition | Aliases
[
  AU           | 1.49598e+11 m   | au, astronomical_unit            ,
  Angstrom     | 1e-10 m         | AA, angstrom                     ,
  cm           | 0.01 m          | centimeter                       ,
  earthRad     | 6.3781e+06 m    | R_earth, Rearth                  ,
  ft           | 0.3048 m        | foot                             ,
  fur          | 201.168 m       | furlong                          ,
  inch         | 0.0254 m        |                                  ,
  jupiterRad   | 7.1492e+07 m    | R_jup, Rjup, R_jupiter, Rjupiter ,
  lsec         | 2.99792e+08 m   | lightsecond                      ,
  lyr          | 9.46073e+15 m   | lightyear                        ,
  m            | irreducible     | meter                            ,
  mi           | 1609.34 m       | mile                             ,
  micron       | 1e-06 m         |                                  ,
  mil          | 2.54e-05 m      | thou                             ,
  nmi          | 1852 m          | nauticalmile, NM                 ,
  pc           | 3.08568e+16 m   | parsec                           ,
  solRad       | 6.957e+08 m     | R_sun, Rsun                      ,
  yd           | 0.9144 m        | yard                             ,
]

This may also be used with the Python “with” statement, to temporarily enable additional units:

>>> with imperial.enable():
...     print(u.m.find_equivalent_units())
      Primary name | Unit definition | Aliases
...

To enable only specific units, use add_enabled_units():

>>> with u.add_enabled_units([imperial.knot]):
...     print(u.m.find_equivalent_units())
      Primary name | Unit definition | Aliases
...