Length of an Arc (in Radian)

How to find the length of an arc whose central angle is in radian: formula, 1 example, and its solution.

Formula

Formula

l = rθ

l: Length of the arc
r: Radius of the arc
θ: Central angle of the arc (in radian)

Use this formula
when the central angle θ is in radian.

When the central angle is in degree measure,
use this formula.

Example

Example

Solution

r = 6
θ = 2π/3

So l = 6⋅[2π/3].

Cancel the denominator 3
and reduce the numerator 6 to, 6/3, 2.

2⋅2π = 4π

So 4π is the answer.