Pronunciation: /ˈreɪ.diən/ Explain

 Click on the blue point and drag it to change the figure. If the measure of a full circle is 2π 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

Full circle
0 rad.none of a full circle
30° rad. of a full circle
45° rad. of a full circle
60° rad. of a full circle
90° rad. of a full circle
180°π rad. of a full circle
270° rad. of a 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 . Example: Convert radians to degrees. ### How to Convert Degrees to Radians

The conversion factor for degrees to radians is . Example: Convert 45° to radians. .

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

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