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# S = rθ 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 ,θ in radians.

### Formula for S =rθ

The picture below illustrates the relationship between the radius, and the central angle in radians. The formula is
s = rθ where s represents the arc length, θ represents the central angle in radians and r is the length of the radius.
Demonstration of the Formual s=rθ
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.
What is the value of the arc length s in the circle pictured below?