# Arc

An arc of a circle is the portion of the circle between two given points on the circle. More generally, an arc is a portion of a smooth curve joining two points.

The measure of a circular arc $AB$ on circle $O$ is defined to be the measure of the central angle $\angle AOB$ which has the arc on its interior. The length of an arc can be calculated by the formula $s = r\theta$, where $r$ is the radius of the circle and $\theta$ is the measure of the arc, in radians. Thus, in particular, the circumference of a circle is given by $C = 2\pi$.