CLUEY RESOURCES
Degrees to Radians
Theory & Practice Questions

Theory
Radian, a circle measure
One radian is the angle that an arc of 1 unit subtends at the centre of a circle of radius 1 unit.
Degrees to radians conversion: 1 degrees = π/180 radians

Radians and Degrees
π^c = 180°
where π^c = π radians
Relationship between radian measure and degrees

Circumference of the circle with radius 1 unit is given by:
C = 2πr
= 2π(1)
= 2π
T
The arc length of the whole circle is 2π.
∴ There are 2π radians in a whole circle.
But there are 360° in a whole circle (angle of revolution).
So 2π^c = 360°
π^c = 180°
Degrees To Radians
To change from degrees to radians: multiply by π/180

Note: Special measure you will use regularly include –

Want a FREE question and answer worksheet?

To get free access to a practice question and answer worksheet for this topic in Mathematics, enter your details below
Practice Question
- Convert 150° into radians.
Solution
- To convert degrees into radians:

Therefore:
150°=150 x π/180 radians
=150π/180 radians
=5π/6 radians
Need some extra help with this topic in Mathematics?
We have a team of expert private tutors ready to give you a hand!
To find out how much tutoring would be and see a recommended learning plan personalised to your student’s needs, get started below.
(takes under 2 minutes)
Enrol today
If you’re ready to get started, enrol online today and get 50% off your first session