Length of an Arc (in Radian)

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

l =

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

Length of an arc

Proof

Length of an Arc (in Radian): Proof of the Formula

Recall the length of an arc formula (in degree):

l = 2πr⋅[(degree)/360]

Change 2π⋅[(degree)/360]
to [π/180]⋅(degree).

[π/180]⋅(degree) = θ (radian)

Radian measure

Example

Find the length of arc AB. Radius: 6. The measure of the central angle: 3pi/2 (rad).

r = 6, θ = 2π/3

l = 6⋅(2π/3)