A unit of measure for angles.
One radian is the angle made at the center of a circle by an arc whose length is equal to the radius of the circle.
Try this Drag the orange dot. Note that the radian is a fixed angle no matter what the size the circle.

The radian is a unit of measure for angles used mainly in trigonometry. It is used instead of degrees. Whereas a full circle is 360 degrees, a full circle is just over 6 radians.

A full circle has 2π radians (Roughly 6.28)
As seen in the figure above, a radian is defined by an arc of a circle. The length of the arc is equal to the radius of the circle. Because of this the radian is a fixed size no matter what the size of the circle is. Drag the orange point and convince yourself this is so.

Recall that the circumference of a circle is 2πR, so that means there are 2π, or roughly 6.28 radians in a full circle. Because a full circle is also exactly 360°, each radian comes out to approximately 57.296°.

To convert between degrees and radians

Given an angle whose measure is D degrees or R radians:
  Exact Approximate
Given degrees (D) 0.017D radians
Given radians (R) 57.3R degrees

Degrees / radians converter

In the boxes below, enter either the number of degrees, or the number of radians (not both) and click on 'convert'.

Common angles in degrees and radians

One of the reasons for using radians is that common angles come out to be convenient fractions of pi, as you can see:
  Exact radians Approximate radians
30° 0.52
45° 0.785
60° 1.048
90° 1.57
180° 3.142
270° 4.71
360° 6.28

Other angle topics


Angle Types

Angle relationships