Arc Length Calculator
Find the arc length of a circle from the radius and angle, the radius and chord, the sector area, or the chord and arc height, with chord and sector area.
Arc length is the distance along the curved edge of a circle between two points. This calculator finds it from whichever pair of measurements you have: radius and central angle, radius and chord, radius and sector area, or — handy for curved walls and arches — the chord and the arc height. It also returns the angle, chord, sector area and the rest of the circle.
How to use this tool
- Pick the pair of values you know.
- Enter them in the matching boxes. Lengths can be in any unit; the results use the same one.
- For the angle option, choose degrees or radians.
- Read the arc length and the related measurements.
Formula
s = r × θ (θ in radians) = 2πr × angle in degrees ÷ 360
r is the radius and θ the central angle. From a chord c: θ = 2·asin(c ÷ 2r), which gives the shorter (minor) arc. From a sector area A: θ = 2A ÷ r². From a chord c and arc height h: r = (c²/4 + h²) ÷ 2h, then θ = 2·atan2(c/2, r − h). The chord is 2r·sin(θ/2), the sector area is r²θ ÷ 2 and the arc height is r(1 − cos(θ/2)).
Example
A radius of 10 cm and a central angle of 60°: θ = 60 × π/180 = 1.047198 rad, so s = 10 × 1.047198 = 10.471976 cm. The chord between the two ends is 2 × 10 × sin 30° = 10 cm, the arc height is 1.339746 cm, and the arc is one sixth (16.6667%) of the 62.831853 cm circumference.
Frequently asked questions
Do I need radians?
Only for the short formula s = rθ. With degrees use s = 2πr × degrees ÷ 360, or let the calculator convert: one radian is about 57.2958°.
What is the difference between arc length and chord length?
The arc follows the curve; the chord is the straight line between the same two points, so it is always shorter. For a 60° arc on a radius of 10, the arc is 10.47 and the chord is exactly 10.
How do I find the length of a curved wall or arch?
Measure straight across the ends (the chord) and the rise of the curve at the middle (the arc height), then use the chord-and-height option. An 8 m span with a 2 m rise has a 5 m radius and an arc of about 9.27 m.
Can the angle be more than 180°?
Yes, up to 360° with the angle and sector-area options, and with the chord-and-height option when the rise is more than the radius. The radius-and-chord option gives the minor arc, and the major arc is listed as the rest of the circle.
Last updated: 2026-10-30