Radians to Degrees​

Theory & Practice Questions



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


The arc length of the whole circle is .


There are radians in a whole circle.


But there are 360° in a whole circle (angle of revolution).

So 2π^c = 360°

π^c = 180°

Radians to Degrees

To change from radians to degrees: multiply by 180/π

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

  1. Convert 5π/6 radians into degrees.
  1. To convert radians into degrees:


5π/6 radians 180/π°5π/6





Need some extra help with this topic in Mathematics?
We have a team of expert private tutors ready to give you a hand!​

More information

Enrol today

If you’re ready to get started, enrol online today and get 50% off your first session