﻿ S= r θ Formula and Equation for the central angle in radian measure

# $$S = r \theta$$ 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.

### 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

Use the $$S = r \theta$$ formula.

S = 3(Π/3) = Π.

##### Problem 2

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

##### Problem 3

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

##### Problem 4

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