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 While you are here..

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