Circle Sector and Segment Area Calculator
Calculate circle sector area, circular segment area, arc length, chord length, sagitta, and perimeter from radius, angle, arc, chord, or segment height.
Sector area and circular segment area
English search intent splits between sector area calculator and circle segment area calculator. This page keeps both because the same known values often produce sector area, triangle area, and the segment cut off by the chord.
| Known values | Use this mode | Returned values |
|---|---|---|
| Radius and central angle | Radius + angle in degrees or radians | Sector area, segment area, arc length, chord, sagitta. |
| Radius and arc length | Radius + arc length | Central angle plus all sector and segment measurements. |
| Radius and chord | Radius + chord | Minor or major segment by the same chord. |
| Radius and segment height | Radius + sagitta | Chord, angle, sector area, and segment area. |
| Chord and segment height | Chord + sagitta | Recovered radius and the full result set. |
Core formulas
A is sector area; r is radius; theta is central angle in radians.
A is minor segment area; theta is central angle in radians.
L is arc length.
c is chord length.
h is sagitta, or segment height.
Minor and major segments
A chord can define a smaller segment and a larger segment. When radius and chord are known, choose minor segment for the smaller cap or major segment for the remaining larger region.
Frequently Asked Questions
Sources and References
- Sector Area CalculatorOmni Calculator
- Circle Segment Area CalculatorMath.net
- Circular SectorWolfram MathWorld
- Circular SegmentWolfram MathWorld
Calculations are based on the listed reference sources. Links open in a new tab.
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