Arc length calculator
Enter the radius and angle and pick its unit to get the arc length, useful for arches and curved paths.
Loading the tool…
Processing and privacy: The result is calculated inside your browser and your data is not sent to any server.
How to use it
- Enter radius, central angle, angle unit and length unit.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Arc length = r × θ with θ in radians, or (angle ÷ 360) × 2πr with the angle in degrees.
Example
Inputs: Radius = 10, Central angle = 180, Angle unit = Degrees, Length unit = Centimeters (cm). Result: Arc length: 31.4159 cm; Angle in radians: 3.1416 rad; Share of the circumference: 50%.
Limits and caveats
- It measures an arc of a single circle with a fixed radius, not general curves or elliptical arcs.
- The length unit choice only labels the results.
Questions about this tool
What is the arc length formula?
Arc length equals the radius times the central angle in radians. A 1 rad arc on a circle of radius 5 is 5 long.
How do I convert degrees to radians?
Multiply the degrees by π ÷ 180, so 180° is π rad, about 3.1416.
What is the difference between arc length and chord length?
The arc runs along the curve, while the chord is the straight line between its ends, so the chord is always shorter.