$$ S = r \theta $$ Formula and Equation

Radian Measure and Arc of a Circle

There is a formula that relates the arc length of a circle of radius, r, to the central angle ,$$ \theta$$ in radians.

Formula for $$ S = r \theta $$

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.

Picture of s = rTheta in a circle

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

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.

Content on this page requires a newer version of Adobe Flash Player.

Get Adobe Flash player

Practice Problem

Problem 1

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

Use the $$ S = r \theta $$ formula
S = 3(Π/3) = Π

Problem 2

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

Use the formula for S = r Θand calculate the intercepted arc:

Problem 3

Calculate the measure of the arc length s in the circle pictured below?

Use the formula for S = r Θ and calculate the intercepted arc:

Problem 4

Calculate the measure of the arc length s in the circle pictured below?

Use the formula for S = r Θ and calculate the solution

back to Radians vs Degrees next to Unit Circle Game