Circle Segment Calculator
Circle Segment: calculate results from explicit inputs, with a formula and worked example.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Euclidean geometry. Use one consistent length unit; areas and volumes use its square and cube. Degenerate shapes are rejected. Very thin shapes may lose floating-point precision. Angles above 180° describe the major segment.
Example Calculation
- Radius: 5 units
- Central angle: 90 °
Radius 5 and angle 90° give segment area approximately 7.1350.
Frequently asked questions
How do I use this calculator?
Enter radius, central angle. The result updates automatically. Use Reset to restore the example values.
What method does it use?
segment area = r²(θ−sin θ)/2; arc = rθ; chord = 2r sin(θ/2), θ in radians. Euclidean geometry. Use one consistent length unit; areas and volumes use its square and cube. Degenerate shapes are rejected. Very thin shapes may lose floating-point precision. Angles above 180° describe the major segment.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.