Circles · §1.4

Arc Length

Arc Length

An arc is a piece of the circle. How long is it? Compare the central angle that defines it to the full 360°. Whatever fraction that is, the arc is the same fraction of the full circumference.

90° arc

So for an arc with central angle θ (in degrees) and radius r:

arc length=θ360°⋅2πr\text{arc length} = \frac{\theta}{360°} \cdot 2\pi r

A 90° arc is a quarter of the circumference. A 180° arc is half — a semicircle. A 360° arc is the whole circle.

Try it
On a circle with circumference 24 in, how long is a 60° arc?
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