Say for eg. r is the radius of the circle. We know that, perimeter (arc length of the circle is 2πr. In this case, the angle described by the circle is 2π).
In above diagram consider s to be the arc length of the circle and angle described by it is θ. If 2πr corresponds to 2π then we have the below expression
2πs = 2πrθ
Solving the above equation we get s=rθ