How to Convert radians to degrees

Radians and degrees are units of measure for angles. As you know, a circle has 2π radians, which is equivalent to 360°; both of these values represent “one round” of the circle. So, 1π radians stands for 180° on the circle, which makes 180/ a perfect converter from radians to degrees. To convert radians to degrees, you simply multiply the radian value by 180/π. If you want to know how to calculate and understand the concept in that calculation, read the article below.

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Understand that 1π radians equals 180 degrees. Before starting the conversion, you must know π radians = 180°, which is equivalent to a semicircle. This is important because you will be using 180/π as the converter. That’s because 1 radian equals 180/π degrees. ^{[1] X Research Source}

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Multiply radians by 180/π to get the measure in degrees. Just that simple! Let’s say you have π/12 radians. To convert to degrees, you must multiply it by 180/π and reduce as necessary. Here’s how: ^{[2] X Research Sources}

/12 x 180/π =
180π/12π 12π/12π =
15°
π/12 radians = 15°

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Practice with a few examples. If you want to be more proficient then practice converting from radians to degrees for more examples. Here are some exercises you can do:

Example 1 : 1/3π radian = /3 x 180/π = 180π/3π 3π/3π = 60°
Example 2 : 7/4π radians = 7π/4 x 180/π = 1260π/4π 4π/4π = 315°
Example 3 : 1/2π radian = /2 x 180/π = 180π /2π 2π/2π = 90°

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Remember that “radian” is different from “π radian”. 2π radians and 2 radians are completely different. As you know, 2π radians is equal to 360 degrees but if you have 2 radians, then you want to convert it to degrees then you will have to do the calculation 2 x 180/π. You should get 360/π or 114.5°. Here’s another answer, because if you don’t work with π radians π won’t cancel out in the equation, thus resulting in a different value. ^{[3] X Research Sources}

Advice

When multiplying, leave pi in radians as the symbol is not a decimal, so you will easily cancel it out during the calculation.
Many graphing calculators have functions to convert units, or you can download a program to convert. Ask your teacher if your calculator has that function.

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