Radian

The angle corresponding to an arc on a circle with length equal to the radius; thus, $180$ degrees is $\pi$ radians; it is approximately ${57}^{\circ }{17}^{\prime }{44}^{″}$. A radian is taken as the unit of measurement of angles in the so-called circular, or radian, measurement of angles. If the circular measure of an angle is $a$ radian, then the angle contains $180a/\pi$ degrees; conversely, an angle of $n^{\circ }$ has circular measure of $\pi n/{180}^{\circ }$ radians.