One Radian

The radian measure of an angle is the ratio of the length of the arc (s) whose centre is at the vertex of the angle to the radius (r).

One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.

If s = r,

$ \displaystyle \text{central angle}=\frac{{\text{length}\ \text{of}\ \text{arc }AB}}{{\text{length}\ \text{of}\ \text{radius}}}=\frac{s}{r}=\frac{r}{r}=1\ \text{radian}$