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'.
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
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