The radian is an angular unit of measurement. Also a ratio, a given number of radians is the arc length associated with a given plane angle divided by the radius of the circle. Therefore, 1 radian (180 degrees/pi) is when an arc length of a circle defined by a central angle is equal to the circle's radius. Given this relationship, you can simply convert between degrees and radians.

If you forget whether to multiply by 180/pi or pi/180 to properly convert, memorize one of the relationships in the previous examples, pi radians = 180 degrees. Then check your work and see if your answer makes sense.

Determine the measurement of your angle in degrees. For example, suppose you have a 90-degree angle.

Convert from degrees to radians by multiplying the number of degrees by pi/180. For a 90-degree angle, multiply 90 by pi/180 to get pi/2. Or, if you had an angle of 270 degrees, you would multiply 270 by pi/180 to get 3*pi/2 radians.

Convert from radians to degrees by multiplying the number of radians by 180/pi. For example, in the example of pi/2 radians, you would multiply pi/2 by 180/pi to get 90 degrees. Or, if you had an angle of pi radians, you would multiply pi by 180/pi to get 180 degrees.

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