# Length of an Arc (in Radian)

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

## Formula

*l* = *rθ**l*: length of an arc*r*: radius of the arc*θ*: radian measure of the arc's central angle

Length of an arc

## Proof

Recall the length of an arc formula (in degree):*l* = 2*πr*⋅[(degree)/360]

Change 2*π*⋅[(degree)/360]

to [*π*/180]⋅(degree).

[*π*/180]⋅(degree) = *θ* (radian)

Radian measure

## Example

*r* = 6, *θ* = 2*π*/3*l* = 6⋅(2*π*/3)