# 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:

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:

## 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?

### Step-by-Step:

# 1

Start with the formula:

Length of arc = ^{θ}⁄_{360°} × 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.