## Converting Angles Between Degrees and Radians

The radian measure of an angle is defined as follows. Draw the angle with its vertex at the center of a circle of radius 1. The radian measure of the angle is the length of the arc (portion of the circle) between the rays of the angle. This is illustrated in the graph below, in which the angle and the arc are drawn in red. By convention, one of the rays is usually drawn on the positive x-axis, and the arc goes in the counter-clockwise direction to the other ray.

Since the circumference of a circle of radius 1 is 2 π, and an angle of 360 degrees goes the entire way around the circle, 360 degrees = 2 π radians, which is about 6.283.

To convert an angle measured in degrees, between 0 and 360, to radians, enter the angle in the Degrees box below and press **Convert to Radians**.

To convert an angle measured in radians, between 0 and 2 π, to degrees, enter the angle in the Radians box and press **Convert to Degrees**.

Copyright 2010 by Paul Trow

Paul Trow's math software.