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

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.What Is an Arc?
An arc is a portion of the circumference.
What Are Radians?
Radians are a way of measuring angles. 1 radian is the angle found when the radius is wrapped around the circle.
Why Does the Formula Work?
An angle in radians can be found using the formula:
Angle = Arc length ⁄ Radius
We can rearrange this formula to make the arc length the subject:
Arc length = Angle × Radius
Arc length = θ × r