The image above represents the length of an arc of a circle.

To compute the length of an arc of a circle, two essential parameters are needed and this parameters are **radius of the circle (r)** and **angle of the circle (α).**

The formula for calculating the length of an arc of a circle:

L = ^{απr} / _{180}

Where;

L = Length of an arc of the circle

α = Angle of the circle

r = radius of the circle

Let’s solve an example:

Find the length of an arc of a circle when the angle of the circle is 90° and the radius of the circle is 20 cm.

This implies that;

α = Angle of the circle = 90°

r = Radius of the circle = 20 cm

L = ^{απr} / _{180}

L = ^{90 x 3.142 x 20} / _{180}

L = ^{5655.6} / _{180}

L = 31.42

Therefore, the **length of an arc of the circle** is **31.42 cm.**

**Calculating the Angle of a Circle using the Radius of the Circle and Length of an Arc of the Circle.**

α = ^{180L} / _{πr}

Where;

L = Length of an arc of the circle

r = Radius of the circle

Let’s solve an example;

Find the angle of the circle when the length of an arc of the circle is 60° and a radius of 140 cm.

This implies that;

L = Length of an arc of the circle = 60°

r = Radius of the circle = 140 cm

α = ^{180L} / _{πr}

α = ^{180 x 60} / _{3.142 x 140}

α = ^{10800} / _{439.88}

a = 24.55

Therefore, the **angle of the circle** is **24.55°.**