Pronunciation: /ˈreɪ.diən/ Explain

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If the measure of a full circle is radians, what is the measure of the angle for 1/2 circle?
Manipulative 1 - Angle Measured in Radians Created with GeoGebra.

A radian is a unit of measure for rotation around a point. 2 π radians is the same rotation as one complete rotation about a circle. The abbreviation for radians is rad.

Common angles in radians and degrees

DegreesRadiansPortion of
Full circle
0 rad.none of a full circle
30°3pi/2 rad.1/12 of a full circle
45°pi/4 rad.1/8 of a full circle
60°pi/3 rad.1/6 of a full circle
90°pi/2 rad.1/4 of a full circle
180°π rad.1/2 of a full circle
270°3pi/2 rad.3/4 of a full circle
360°rad.One full circle
Table 1: Common angles in radians and degrees

How to Convert Radians to Degrees

One complete rotation about a circle is rad. or 360°. This means rad. = 360°. So, the conversion factor is 360 degrees/2pi radians = 180 degrees / pi.. Example: Convert pi/2 radians to degrees. (pi/2) rad. * (180 degrees/pi) = (pi@crossed out@/2) rad. * (180 degrees)/(pi@crossed out@) = (180/2) degrees = 90 degrees.

How to Convert Degrees to Radians

The conversion factor for degrees to radians is 2pi radians/360 degrees = pi rad./180 degrees.. Example: Convert 45° to radians. 45°*(pi rad)/(180 deg) = 45@crossed out@ °*(pi rad)/(4*45@crossed out@ degrees) = pi/4 rad..


  1. McAdams, David E.. All Math Words Dictionary, radian. 2nd Classroom edition 20150108-4799968. pg 149. Life is a Story Problem LLC. January 8, 2015. Buy the book

More Information

  • McAdams, David E.. Angle. allmathwords.org. Life is a Story Problem LLC. 3/12/2009. http://www.allmathwords.org/en/a/angle.html.

Cite this article as:

McAdams, David E. Radian. 5/3/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/r/radian.html.

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Revision History

5/3/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/4/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra app. (McAdams, David E.)
5/5/2011: Initial version. (McAdams, David E.)

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