ETYM From Radius.
The angle between two radii of a circle such that the length of the arc between them is equal to the radius. The circumference of a circle is equal to 2p times the radius, so one radian contains 360/(2p) = 180/p = approximately 57.2958 degrees. Conversely, multiplying the number of degrees by p/180 gives the number of radians; 360 degrees equals 2p radians. See the illustration.
Si unit (symbol rad) of plane angles, an alternative unit to the degree. It is the angle at the center of a circle when the center is joined to the two ends of an arc (part of the circumference) equal in length to the radius of the circle. There are 2p (approximately 6.284) radians in a full circle (360ş).
One radian is approximately 57ş, and 1ş is p/180 or approximately 0.0175 radians. Radians are commonly used to specify angles in polar coordinates.
The unit of plane angle adopted under the System International d'Unites; equal to the angle at the center of a circle subtended by an arc equal in length to the radius (approximately 57.295 degrees); SYN. rad.