How to Find the Length of an Arc of a Circle

Finding the Length of an Arc of a Circle

The length of an arc of a circle is given by the formula:

length of arc equals angle divided by 360 all times 2 times pi times radius

In this formula, θ is the angle (in degrees) subtended by the arc and r is the radius of the circle. The image below shows what we mean by the length of an arc:

angle, arc and radius on a circle

How to Find the Length of an Arc of a Circle

Finding the length of an arc of a circle is easy.

Question

What is the length of the arc with an angle of 60° and a radius of 5 cm, as shown below?

arc length with an angle of 60 degrees and a radius of 5 cm

Step-by-Step:

1

Start with the formula:

Length of arc = θ360° × 2πr

Don't forget: π is pi (≈ 3.14) and / means ÷.

2

Substitute the angle and the radius into the formula. In our example, θ = 60° and r = 5.

Length of arc = 60°360° × 2 × π × 5

Length of arc = (60° ÷ 360°) × 2 × 5 × π

Length of arc = 5.2 cm

Answer:

The length of an arc of a circle with a radius of 5 cm, which is subtended by an angle of 60°, is 5.3 cm.

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The slider below shows another real example of how to find the length of an arc of a circle.

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See Also

What is a circle? What is an angle? What is pi? What are degrees? Finding the circumference of a circle What is a full angle?