Radian

The radian is the SI supplementary unit of angle. It is defined as the angle subtended at the center of a circle by an arc of circumference equal in length to the radius of the circle.

There are 2&pi (about 6.283185) radians in a complete circle. One radian is equal to 180°/π or approximately 57.29578°.

In calculus, the use of radians leads to the simple identity

which is the basis of many elegant identities in mathematics.

Conversion of degrees to radians can be carried out using the formula

For measuring solid angles, see steradian.