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Radian

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'.
Degrees:
Radians:
 

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

General

Angle Types

Angle relationships