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 an arc, theta: Measure of an arc's central angle (= Measure of an arc)

l = 2πr⋅(θ/360)

l: Length of an arc
π = 3.141592...
r: Radius of an arc
θ: Measure of an arc's central angle
(= Measure of an arc)

2πr is the circumference of the whole circle.

θ/360 is the ratio of
(Arc's central angle, θ)/(Circle's central angle, 360).

Example

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

r = 6
θ = 120

So l = 2π⋅6⋅(120/360).

2π⋅6 = 12π
120/360 = 1/3

So l = 12π⋅(1/3).

12⋅(1/3) = 4

So l = 4π.