The length of an arc on a circle depends on both the angle of rotation and the radius length of the circle.we defined a radian as the length of the arc the measure of an angle θ in radians is defined as the length of the arc cut off by one radius length, so that a half-rotation is π radians, or a little more than 3 radius lengths around the circle. What if the radius is 4 cm? The length of the half-circle arc would be π radius lengths, or 4π cm in length.
This results in a formula that can be used to calculate the length of any arc.where s is the length of the arc, r is the radius, and θ is the measure of the angle in radians.Solving this equation for θ will give us a formula for finding the radian measure given the arc length and the radius length: