The radian is a unit of angular measure defined such that an angle of one radian subtended from the center of a unit circle produces an arc with arc length 1.

A full angle is therefore radians, so there are per radians, equal to or 57./radian. Similarly, a right angle is radians and a straight angle is radians.

Radians are the most useful angular measure in calculus because they allow derivative and integral identities to be written in simple terms, e.g.,

for measured in radians.

Unless stated otherwise, all angular quantities considered in this work are assumed to be specified in radians.