How Do You Convert 10 Degrees to Radians?

A radian is a unit of angular measure widely used in many branches of mathematics and physics. One radian is equal to the measure of an angle at the center of a circle with an arc that is equal in length to the radius of that circle. Since the perimeter of a circle is found by doubling the radius and multiplying by pi, one radian is equal to 180 degrees divided by pi, or roughly 57.2958 degrees.

  1. Multiply number of degrees by pi / 180

    To find the radian equivalent of 10 degrees, multiply 10 by pi / 180. The result, 10 pi / 180, simplifies to pi / 18.

  2. Approximate for pi and divide by 18

    If pi / 18 is not a workable answer, choose an approximate value for pi and divide by 18. Since pi is an irrational number, it has no precise numerical equivalent, but an approximation can give a fairly accurate answer. For example, 3.14 / 18 equals approximately 0.174.

  3. Use a calculator to divide pi by 18

    Many calculators include a pi function that provides a very accurate approximation of pi. Using a calculator to divide pi by 18 gives an answer of approximately 0.174532925. This is a very close approximate value for the number of radians in 10 degrees.