Definition of a radian
A radian is a unit of angular measure. A revolution of a circle has an angle of 2π radians.

A radian is a unit of measuring angles. It is shown by the symbol "rad"[1] or, less often, c (for circular measure). The radian was once an SI supplementary unit, but was changed to a derived unit in 1995. A radians arc length is equal to the radii from the circle it is part of.

## Usage

Most people who do mathematics or physics use radians, rather than degrees, because some kinds of calculations, mostly in trigonometry and calculus, are simpler when using radians rather than degrees. Thus, most calculations related to angular frequency (such as angular velocity) use radians per second.

People who look through a telescope or sniper scope often use milliradians to describe distances as seen through it.

## Conversion

1 radian is equal to about 57.3°. There are 2π radians (about 6.28 radians) in a full circle.[2] The formula for turning radians to degrees and vice versa is:[3]

${\displaystyle 2\pi {\mbox{ rad}}=360^{\circ }}$
${\displaystyle 1{\mbox{ rad}}={\frac {360^{\circ }}{2\pi }}={\frac {180^{\circ }}{\pi }}\approx 57.29577951^{\circ }}$

or:

${\displaystyle 360^{\circ }=2\pi {\mbox{ rad}}}$
${\displaystyle 1^{\circ }={\frac {2\pi }{360}}{\mbox{ rad}}={\frac {\pi }{180}}{\mbox{ rad}}\approx 0.01745329{\mbox{ rad}}}$

we can also say that:

${\displaystyle x{\mbox{ rad}}=\left({\frac {180x}{\pi }}\right)^{\circ }}$.

## References

1. "List of Geometry and Trigonometry Symbols". Math Vault. 2020-04-17. Retrieved 2020-08-31.{{cite web}}: CS1 maint: url-status (link)
2. "Radian - math word definition - Math Open Reference". www.mathopenref.com. Retrieved 2020-08-31.
3. Weisstein, Eric W. "Radian". mathworld.wolfram.com. Retrieved 2020-08-31.