What is a radian?A radian is the measure of an angle at the centre of a circle subtended by an arc, whose arc length is equal to the radius of the circle: Not exactly what this means.

When I am looking for arc length I can find the circumference around the circle then take the fraction of the angle that I am given to the whole circle.

If I use the formula S=(thata)r

thata has to be in terms of radians-- why?