Radian Measure

Radian Measure

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


(radian) = (pi/180)*(degree)

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.


Radian Measure: Proof of the Formula

Recall the length of an arc formula:
l = 2πr⋅(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).


Find the radian measure of each angle. 1. 360 degree, 2. 180 degree, 3. 30 degree, 4. 45 degree, 5. 60 degree, 6. 90 degree

To find the radian measure,
multiply (π/180) to the degree measure.

So 360º = 2π (rad).

Just like this,
you can write the other angles
in radian measure.