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How to Change Degrees to Radians

The computation required for changing degrees to radians isn't difficult. The computation involves a few tricks, though, and the format is important. You don't usually write the radian measures with decimal values unless you've multiplied through by the decimal equivalent for pi.

To change a measure in degrees to radians, start with the basic proportion for the equivalent angle measures:


For example, here's how you change a measure of 40 degrees to radians:

  1. Put the 40 in place of the first numerator in the proportion.

  2. Reduce the fraction on the left.

  3. Multiply each side of the proportion by pi.

  4. Simplify the work.


This example shows that 40 degrees is equivalent to


You leave the radian measure as a fraction reduced to lowest terms.

Check out another example: Change a measure of –36 degrees to radians.

  1. Put the –36 in in the proportion.

  2. Reduce the fraction on the left.

  3. Multiply each side of the proportion by pi.

  4. Simplify the work.


So you see, –36 degrees is equivalent to


Having a negative angle is fine. You leave the expression as a fraction; don't change it to a decimal form.

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