The radian is a measure unit of angle used in the higher mathematics. The magnitude of an angle $\alpha$ is one radian, if the arc corresponding the angle $\alpha$ as a central angle of a circle is equally long as the radius of the circle. Thus, a radian is equal to $\frac{180}{\pi}$ degrees. It is in degrees, minutes and seconds approximately $57^{\mathrm{o}}\,17'\,44.80625''.$

In degrees, a circle has 360 degrees, while in radians a circle has $2\pi$ radians. In fact, many angles of equilateral polygons are equal to a multiple of $\pi$ divided by some integer: for example, the interior angle of an equilateral triangle's vertex is $\frac{\pi}{3}$ , while the interior angle of an equilateral pentagon's vertex is $\frac{3\pi}{5}$ .