Arc Length Definition

In geometry, an arc length, also known as the length of an arc, is defined as the range interval or distance among the two points of a circle’s circumference or curve.

In mathematical form, an arc length of a circle is written as: s = θ × r Where, s = length of an arc. θ = angle formed in an arc (measured in radians) and r = radius of a circle (measured in cm).

For a more precise understanding, check out the picture given below:

arc length


Table Of Contents

Formula Of Arc Length

To calculate arc length in degree, you can use this formula:

s = (θ × π/180) × r


θ = degree

r = radius


To calculate arc length, you can use our Arc Length Calculator.


For more precise understanding, let us have an example below:

If a radius of an arc = 10cm and the angle formed in it is 0.349 radians, you can find the length of an arc using the formula listed below:

Given data

r = 10 cm
θ = 0.349 rad

To Find

Arc length = ?


To find out the arc length, we will use the formula listed below:

s = θ × r

Putting values in the formula:

s = 0.349 x 10 = 3.49 cm