How to Convert Radians to Degrees

By Ainsley Patterson; Updated April 24, 2017

A radian is the measurement of the angle created when you wrap the radius of a circle around its circumference. Sometimes when you solve a trigonometry problem involving the measurement of angle, you will be asked to put your answer in radians, and sometimes you will be asked to put your answer in degrees. Other times, the problem itself might be to convert radians to degrees. Here is a guide for converting radians to degrees so that you can solve these types of problems with ease.

Learn the equation to convert radians to degrees: R * (180 / ?) = D R stands for radians, and D stands for degrees.

Plug the measurement of your angle in radians into the equation above in place of the R. For example, you are told to convert the measurement of an angle from 2 radians to a measurement in degrees. Begin by replacing the R in the above equation with 2, which leaves you with this: 2 * (180 / ?) = D

Do the division inside of the parentheses, according to the order of operations. In the example, simplify the equation into the following: 2 * 57.296 = D Round the answer you get from doing the division inside the parentheses to the nearest thousandth.

Multiply out the rest of the equation to get the final answer. To finish the conversion example, multiply out the rest of the equation as follows: 2 * 57.296 = 114.592 This is rounded to the nearest thousandth.

Attach units to your final answer. It is so important to put your answer in terms of units whenever possible, especially when you are doing a conversion.
For the example problem, the final answer is that an angle that measures 2 radians measures 114.592 degrees.

Tip

If you need to convert from degrees to radians, then you can simply plug in your value for the D in the equation given above and then solve for R, or you can use the equation R = D * (? / 180), where D is still degrees and R is still radians. Most calculators will do this conversion for you, but you should always know how to do what your calculator will do for you on your own.

Warning

Don't forget to put your answer in terms of units; most math teachers will mark you down for leaving the units off your final answer.

About the Author

Based in Ypsilanti, Mich., Ainsley Patterson has been a freelance writer since 2007. Her articles appear on various websites. She especially enjoys utilizing her more than 10 years of craft and sewing experience to write tutorials. Patterson is working on her bachelor's degree in liberal arts at the University of Michigan.