Arc Length Calculator
Find the length of an arc from the radius and central angle, plus the chord and sector area.
About the Arc Length Calculator
An arc is part of a circle's circumference. Its length is proportional to the angle it spans. With the angle in radians the formula is simply radius × angle.
The formula
L = r × θ (θ in radians)
- θ in degrees
- L = (θ ÷ 360) × 2πr
- Chord
- 2r × sin(θ/2)
- Sector area
- ½r²θ
Worked example
r = 10, θ = 60°
- θ = π/3 ≈ 1.0472
- L ≈ 10.472
Questions people ask
What's the difference between arc and chord?
The arc follows the curve; the chord is the straight line between its ends, always a little shorter.
Why use radians?
One radian is the angle where the arc equals the radius, which makes the formula L = rθ.