Radian angle measure

Let there be a central angle n °. The expanded angle corresponds to the length of the semicircle πR. Hence, an angle of 1 ° corresponds to an arc of length πR / 180, and an angle of n ° corresponds to an arc of length.



Radian measure of the angle is the ratio of the length of the corresponding arc to the radius of the circle. Consequently,



From this it is seen that the radian measure of the angle is obtained from the degree multiplication by π / 180 °.