Radian Measure

How to change angle in degree measure to radian measure and vice versa: definition, formula, 2 examples, and their solutions.

Definition

Definition

Radian is another way
to write the measure of an angle.

Remember this definition:
π radian = 180 degrees.

Formula

Formula

To find radian measure from degree measure,
multiply [π/180].

Example 1

Example

Solution

The given angle is in degree measure:
30 degrees.

To change this to radian measure,
multiply [π/180].

Cancel the numerator 30
and reduce the denominator 180 to, 180/30, 6.

Then you get π/6.

So 30 degrees is π/6 radian.

You don't have to write the radian unit [rad].
So π/6 is the answer.

Example 2

Example

Solution

The given angle is in radian measure:
π/4.

Set the degree measure θ.

Then θ⋅[π/180] = π/4.

Divide both sides by [π/180].

Then θ = [π/4]⋅[180/π].

Cancel π factors.

Cancel the denominator 4
and reduce the numerator 180 to, 180/4, 45.

So the right side is 45.

So π/4 radian is 45 degrees.