# Combining and Defining Units¶

## Basic example¶

Units and quantities can be combined together using the regular Python numeric operators:

```
>>> from astropy import units as u
>>> fluxunit = u.erg / (u.cm ** 2 * u.s)
>>> fluxunit
Unit("erg / (cm2 s)")
>>> 52.0 * fluxunit
<Quantity 52. erg / (cm2 s)>
>>> 52.0 * fluxunit / u.s
<Quantity 52. erg / (cm2 s2)>
```

## Fractional powers¶

Units support fractional powers, which retain their precision through
complex operations. To do this, it is recommended to use
`fractions.Fraction`

objects:

```
>>> from fractions import Fraction
>>> Franklin = u.g ** Fraction(1, 2) * u.cm ** Fraction(3, 2) * u.s ** -1
```

Note

Floating-point powers that are effectively the same as fractions
with a denominator less than 10 are implicitly converted to
`Fraction`

objects under the hood. Therefore, the
following are equivalent:

```
>>> x = u.m ** Fraction(1, 3)
>>> x.powers
[Fraction(1, 3)]
>>> x = u.m ** (1. / 3.)
>>> x.powers
[Fraction(1, 3)]
```

## Defining units¶

Users are free to define new units, either fundamental or compound,
using the `def_unit()`

function:

```
>>> bakers_fortnight = u.def_unit('bakers_fortnight', 13 * u.day)
```

The addition of a string gives the new unit a name that will show up when the unit is printed:

```
>>> 10. * bakers_fortnight
<Quantity 10. bakers_fortnight>
```

Creating a new fundamental unit is also possible:

```
>>> titter = u.def_unit('titter')
>>> chuckle = u.def_unit('chuckle', 5 * titter)
>>> laugh = u.def_unit('laugh', 4 * chuckle)
>>> guffaw = u.def_unit('guffaw', 3 * laugh)
>>> rofl = u.def_unit('rofl', 4 * guffaw)
>>> death_by_laughing = u.def_unit('death_by_laughing', 10 * rofl)
>>> (1. * rofl).to(titter)
<Quantity 240. titter>
```

Users can see the definition of a unit and its decomposition via:

```
>>> rofl.represents
Unit("4 guffaw")
>>> rofl.decompose()
Unit("240 titter")
```

By default, custom units are not searched by methods such as
`find_equivalent_units()`

. However, they
can be enabled by calling `add_enabled_units()`

:

```
>>> kmph = u.def_unit('kmph', u.km / u.h)
>>> (u.m / u.s).find_equivalent_units()
There are no equivalent units
>>> u.add_enabled_units([kmph])
<astropy.units.core._UnitContext object at ...>
>>> (u.m / u.s).find_equivalent_units()
Primary name | Unit definition | Aliases
[
kmph | 0.277778 m / s | ,
]
```