What Is the Equation to Convert Degrees to Radians?


Quick Answer

The equation used to convert degrees to radians is rad = (deg x pi)/180, where rad stands for radians, deg is degrees and pi is equal to 3.142. Radians and degrees are ways to measure an angle in a circle.

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Full Answer

A simple example using this equation is to convert 60 degrees into radians. By substituting 60 degrees into the equation, one finds that radians = (60 x pi)/180 = pi/3 = 3.142/3 = 1.047 radians.

Students can manipulate the equation rad = (deg x pi)/180 such that they multiply both sides of the equation by 180 degree and divide by pi to get the new equation (rad x 180)/pi = deg. This is the equation to convert from radians to degrees. As a check that this equation is correct, students can use the result of 1.047 radians in this equation, which should give the answer 60 degrees.

A circle has 360 degrees, and 2 pi radians equals 360 degrees. From this relationship, it is easy to see that pi radians is then equal to 180 degrees.

To find the approximate radian measurement of angles like 2 pi or pi/2, one has to multiply by the value of pi given as 3.142 to get 6.283 and 1.571 respectively.

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