# Radian Measure

How to change degree measure into radian measure: formula, proof, examples, and their solutions.

## Formula

Radian is a way to write the measure of an angle

by the length of the unit circle's arc.

(Unit circle: *r* = 1)

To change the degree measure to radian measure:

(radian) = (*π*/180)⋅(degree).

The unit of radian measure is written as 'rad'.

But, mostly, it is omitted.

## Proof

Recall the length of an arc formula:*l* = 2*πr*⋅(*θ*/360)

The definition of radian measure

is the length of the unit circle's arc.

So *l* = (radian).

The unit circle's radius is 1.

So *r* = 1.

The arc formula's *θ* is in degree measure.

So *θ* = (degree).

Then (radian) = (*π*/180)⋅(degree).

## Examples

To find the radian measure,

multiply (*π*/180) to the degree measure.

So 360º = 2*π* (rad).

Just like this,

you can write the other angles

in radian measure.