The picture below illustrates the relationship between the radius, and the central angle in radians. The formula is $$ S = r \theta $$ where s represents the arc length, $$ S = r \theta$$ represents the central angle in radians and r is the length of the radius.

Demonstration of the Formula $$ S = r \theta$$

The interative demonstration below illustrates the relationship between the central angle of a circle, measured in radians, and the length of the intercepted arc. Just click and drag the points.

Practice Problem

Problem 1

What is the value of the arc length S in the circle pictured below?