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
used mainly in
It is used instead of
Whereas a full circle is 360 degrees, a full circle is just over 6 radians.
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
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.
A full circle has 2π radians (Roughly 6.28)
Recall that the
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:
|Given degrees (D)
|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:
While you are here..
... I have a small favor to ask. Over the years we have used advertising to support the site so it can remain free for everyone.
However, advertising revenue is falling and I have always hated the ads. So, would you go to Patreon and become a patron of the site?
When we reach the goal I will remove all advertising from the site.
It only takes a minute and any amount would be greatly appreciated.
Thank you for considering it! – John Page
Become a patron of the site at patreon.com/mathopenref
Other angle topics
(C) 2011 Copyright Math Open Reference. All rights reserved