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How to Change Radians to Degrees

Many math problems require you to change measurements from radians to degrees. You often perform mathematical computations in radians, but then convert to degrees so the final answers are easier to visualize and comprehend.

You can use a nifty little proportion to change from radians to degrees. In this proportion, the Greek letter theta, θ, represents the name of the angle. Putting the superscripts ° and R on θ makes the angle stand for the measure in degrees and radians, respectively.

image0.png

This proportion reads: “The measure of angle θ in degrees divided by 180 is equal to the measure of angle θ in radians divided by π. Remember that p is about 3.141592654.

For example, to change

image1.png

to a degree measure, you would follow these steps:

  1. Put the radian measure in place of the θR in the proportion.

    image2.png
  2. Simplify the complex fraction on the right by multiplying the numerator by the reciprocal of the denominator.

    image3.png
  3. Multiply each side of the proportion by 180.

    image4.png
  4. Reduce and simplify the fraction on the right.

    image5.png
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