How to Convert Degrees to radians

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Degrees and radians are two units of angle measurement. ^{[1] X Research Source} A circle has 360 degrees, which is equivalent to 2π radians, so 360° and 2π radians represent the numerical value of “one turn” of the circle. ^{[2] X Research Source} If you’re still confused don’t worry, with just a few simple steps you can easily convert degrees to radians and vice versa.

Steps

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Write the number of degrees that you want to convert to radians. ^{[3] X Research Source} Let’s practice with some of the following examples so you can understand the concept:

Example 1 : 120°
Example 2 : 30°
Example 3 : 225°

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Multiply the number of degrees by π/180. To understand why you need to do this, you should know that 180 degrees is equal to π radians. Therefore, 1 degree is equal to (π/180) radians. From there, all you need to do is multiply the number of degrees you want to convert by π/180 to convert degrees to radians. The answer is in radians so you can remove the degree symbol. Here’s how: ^{[4] X Research Sources}

Example 1 : 120 x /180
Example 2 : 30 x /180
Example 3 : 225 x /180

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Do mathematics. Do the math by multiplying the number of degrees by π/180. Similar to multiplying two fractions: the first has degrees as the numerator and “1” as the denominator, the second has π as the numerator and 180 as the denominator. We do the following:

Example 1 : 120 x /180 = 120π/180
Example 2 : 30 x /180 = 30π/180
Example 3 : 225 x /180 = 225π/180

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Compact. Now you need to reduce each fraction to its simplest form to get the final answer. Find the largest number that is divisible by both the numerator and the denominator to reduce the fraction. In example 1, the number to look up is 60; in example 2 it’s 30 and in example 3 it’s 45. But don’t rush; you can try first by dividing the numerator and denominator by 5, 2, 3 or any number that works. Here’s how to do it:

Example 1 : 120 x /180 = 120π/180 60/60 = 2/3π radians
Example 2 : 30 x /180 = 30π/180 30/30 = 1/6π radian
Example 3 : 225 x /180 = 225π/180 45/45 = 5/4π radians

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Write the answer. To finish the math cleanly, you can write the original angle measure out when converting to radians. Do the following:

Example 1 : 120° = 2/3π radian
Example 2 : 30° = 1/6π radian
Example 3 : 225° = 5/4π radian

Steps

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