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How to Change Radians to Degrees

You use the same basic proportion to change radians to degrees as you do for changing degrees to radians. The computation required for changing radians to degrees isn't difficult. For example, to change

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radians to a degree measure:

  1. Put the radian measure in the proportion.

    image1.jpg
  2. Simplify the complex fraction on the right by multiplying the numerator by the reciprocal of the denominator.

    image2.jpg
  3. Multiply each side of the proportion by 180.

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  4. Reduce and simplify the fraction on the right.

    image4.jpg

    So,

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    radians is equivalent to 15 degrees.

Here's another example: Change 1.309 radians to degrees.

Change this radian measure to a decimal by multiplying through by a decimal equivalent of pi, which is approximately 3.1416. You use this same decimal equivalent to solve the problem.

  1. Put the radian measure in the proportion.

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  2. Change the pi to a decimal approximation. In this case, use four decimal places.

    image7.jpg
  3. Multiply each side of the proportion by 180.

    image8.jpg
  4. Reduce the fractions, and simplify the value on the right.

    image9.jpg

This result came out to be a nice number. Sometimes, however, you have a decimal answer for the degrees. Actually, you get a decimal more than sometimes — you usually get one.

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