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# 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 1541-2021 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
Zi | zebi- | 2 ** 70
Yi | yobi- | 2 ** 80

## 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, Å                  ,
      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
    ...