Sector Area Calculator
Calculate the area of a circular sector and segment, and the sector perimeter, from radius and angle.
Your inputs
Results
Sector area
78.539816 m²
- Segment area (between chord and arc)
- 28.539816 m²
- Sector perimeter
- 35.707963 m
✓Exact calculation — rounded only for display
What this calculator does
A sector is a pie-slice; a segment is the region between a chord and its arc.
Formula and method
Sector = ½ r² θ; Segment = ½ r² (θ − sin θ); Perimeter = 2r + r θ
Worked example
Calculated by this tool with its default inputs:
Inputs
- Length unit: Metres
- Radius: 10
- Central angle: 90
- Angle unit: Degrees
Results
- Sector area: 78.539816 m²
- Segment area (between chord and arc): 28.539816 m²
- Sector perimeter: 35.707963 m
How to read the results
At 360°, the sector is the whole circle.
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
What is a circular segment?
The part of a circle cut off by a chord.
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