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.
About the Author
Kaitlyn Schwalje began writing in 2004 for her high school literary magazine and then focused her interests after publishing an article on topics of neuroscience in her college's journal of science, "The Triple Helix." Schwalje graduated from Carnegie Mellon University with a Bachelor of Science degree in physics in May of 2010.