The measure of an angle is determined by the amount of rotation from the initial side to the terminal side. One way to measure angles is in radians. To define a radian, use a central angle of a circle (an angle whose vertex is the center of the circle). One radian is the measure of a central angle that intercepts an arc s equal in length to the radius r of the circle.
Since the circumference of a circle is 2πr, one revolution around a circle of radius r corresponds to an angle of 2π radians because .