 The definition of one radian is the angle for which these three lengths are all equal. So if these lengths are both one, then at an angle of one radian, the length of this arc will also be one. If I now increase the angle to two radians, what will the length of the arc be? Well the length of the arc is always equal to the radius times the radian angle. So on the unit circle, the length of this arc will be two, just like the radian angle. The diameter of a circle is twice the length of the radius. The ratio between a circle's diameter and its circumference is pi. So the circumference of the whole circle is equal to two times the length of the radius times pi. When the radius of the circle is one, the radian angle is equal to the circumference of the circle. Therefore, there are two pi radians in a circle.