Length of an Arc

Length of an Arc

How to find the length of an arc: formula, example, and its solution.

Formula

l = 2*pi*r*((theta)/360), l: length of an arc, pi: 3.141592..., r: radius of the arc, theta: measure of the arc's central arc (= measure of the arc)

l = 2πr⋅(θ/360)

l: length of an arc
π: 3.141592...
r: radius of the arc
θ: measure of the arc's central angle
(= measure of the arc)

2πr: circumference of the circle
θ/360: ratio of (arc)/(circumference)

Example

Find the length of arc AB. Radius: 6. The measure of the central angle: 120.

r = 6, θ = 120

l = 2π⋅6⋅(120/360)