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