How it works
A circular segment is bounded by a chord and its arc, rather than by two radii. Convert the degree angle to radians internally, then subtract the isosceles triangle area from the sector area. Radius 2 with angle 90° gives segment area π − 2. The supported angle range selects the minor segment, including the semicircle at 180°.
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| Circle radius | 5 | Enter a numeric value. Distance from the centre to the edge; half the diameter. Must be greater than zero. |
| Central angle | 90 ° | Required unit: °. Use a non-negative value. Allowed range: 0–180. |
Worked example
Show example inputs and results
This example is generated by the same calculation engine using the starting values in the form. Your own inputs produce your own result.
- Circle radius
- 5
- Central angle
- 90 °
Complete example results
- Minor segment area
- 7.13495408
- Chord length
- 7.07106781
- Arc length
- 7.85398163
Reading the result
Enter lengths in the same unit. Area uses the square of that unit and volume its cube. Height is perpendicular to the base; use a sloping side only when the input explicitly asks for it.
Questions and answers
Can I use the example values for my own calculation?
The example values illustrate the calculation. Replace every input with your own information, especially dates, rates and the selected operation.
How do I obtain the major segment area?
Subtract the returned minor segment area from πr². The chord is shared by the two complementary segments; their arc lengths are different.
Why are some results rounded?
Results display up to 8 decimal places. Calculations use the unrounded values; very small values use scientific notation. JavaScript floating-point arithmetic can introduce tiny rounding differences.
Are my inputs sent to a server?
The calculator processes inputs in your browser. Its code does not send your values to a server.
Method sources: mathworld.wolfram.com