Radian Measure

A central angle of a circle that is subtended by an arc equal in length to the circle's radius, is said to have a measure of one radian, denoted 1 rad.

It follows that the radian measure of a central angle $\theta$ subtended by an arc of length $s$ can be found by determining how many times the length of the radius $r$ is contained in the arc length $s.$ This suggests the formulas ($s,r$ in the same units, $\theta$ in radians:)

$$\theta = \frac{s}{r}$$

$$s = r\theta.$$

Note: If the units of an angle's measure are not specified, in most contexts radians are the default.