# Length of an Arc

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

## Formula

*l* = 2*πr*⋅(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)

2*πr* is the circumference of the whole circle.

θ/360 is the ratio of

(Arc's central angle, θ)/(Circle's central angle, 360).

## Example

*r* = 6*θ* = 120

So *l* = 2*π*⋅6⋅(120/360).

2*π*⋅6 = 12*π*

120/360 = 1/3

So *l* = 12*π*⋅(1/3).

12⋅(1/3) = 4

So *l* = 4*π*.