# 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:

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:

## 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?

### 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.