Arc Length Calculator
Calculate the arc length and chord length of a circle segment from its radius and central angle in degrees or radians.
Your inputs
Results
Arc length
15.707963 m
- Chord length
- 14.142136 m
- Share of the full circle
- 25%
✓Exact calculation — rounded only for display
What this calculator does
Arcs are parts of a circle’s circumference — for curved paths, bends and design.
Formula and method
Arc length s = r θ (θ in radians); chord = 2r sin(θ ÷ 2)
Worked example
Calculated by this tool with its default inputs:
Inputs
- Length unit: Metres
- Radius: 10
- Central angle: 90
- Angle unit: Degrees
Results
- Arc length: 15.707963 m
- Chord length: 14.142136 m
- Share of the full circle: 25%
How to read the results
A quarter circle (90°) has an arc a quarter of the circumference.
Assumptions and limitations
- Use one length unit consistently; areas are in square units and volumes in cubic units of that length.
Quantities and costs are planning estimates. Add sensible allowances, and check with suppliers, carriers or professionals before buying, shipping or building.
Questions
How do I convert degrees to radians?
Multiply by π ÷ 180.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 3 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Inputs are added to a share link only if you choose to include them. Privacy policy