Radian

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The radian is the SI derived 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.

An angle measuring 1 radian subtends an arc equal in length to the radius of the circle

There are 2&pi (about 6.283185) radians in a complete circle, so:
2π rad = 360°
1 rad = 360/(2π)° = 180/π° (approximately 57.29578ÃÂ°).

or:
360° = 2π rad
1° = 2π/360 rad = π/180 rad

In calculus, angles must be represented in radians in trigonometric functions, to make identities and results as simple and natural as possible. For example, the use of radians leads to the simple identity

which is the basis of many elegant identities in mathematics.

The radian was formerly an SI supplementary unit, but this category was abolished from the SI system in 1995.

For measuring solid angles, see steradian.

Radian

See also