How to Find the Length of an Arc of a Circle (Radians)

Finding the Length of an Arc of a Circle (Radians)

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

length of arc equals radius times angle in radians

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

arc, angle and radius

How to Find the Length of an Arc of a Circle (Radians)

Finding the length of an arc of a circle, when the angle is in radians, is easy.

Question

What is the length of the arc with an angle of 1 radian and a radius of 5 cm, as shown below?

arc subtended by 1 radian with a radius of 5 cm

Step-by-Step:

1

Start with the formula:

Length of arc = rθ

2

Substitute the radius and the angle into the formula. In our example, r = 5 and θ = 1.

Length of arc = 5 × 1

Length of arc = 5 cm

Answer:

The length of an arc of a circle with a radius of 5 cm, which is subtended by an angle of 1 radian, is 5 cm.

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The slider below shows another real example of how to find the length of an arc of a circle when the angle is in radians.

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See Also

What is a circle? What is an angle? What are radians?