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.
- 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.
- 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.
- 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.