The “pizza slice” of a circle: its area, arc, chord and segment.
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A sector is the part of a circle between two radii — a slice of pizza or a pie-chart wedge. Its area and arc length are the same fraction of the whole circle as its angle is of 360°. The segment is the part between the chord and the arc.
Enter the radius and angle. The calculator gives the sector area, arc length, perimeter, chord length, segment area and the share of the circle, using ½r²θ and rθ with θ in radians (degrees are converted).
| Radius r | 10 |
| Central angle θ | 60 |
| Angle in | Degrees |
| Length unit | cm |
| Sector area | 52.359878 cm² |
| Arc length | 10.471976 cm |
| Perimeter of the sector | 30.471976 cm |
| Chord length | 10 cm |
| Segment area (between chord and arc) | 9.0586074 cm² |
| Angle | 60° = 1.0471976 rad |
| Share of the circle | 16.6667% (circle area 314.15927 cm²) |
Area 52.359878 cm².
| Radius r | 5 |
| Central angle θ | pi/2 |
| Angle in | Radians |
| Length unit | m |
| Sector area | 19.634954 m² |
| Arc length | 7.8539816 m |
| Perimeter of the sector | 17.853982 m |
| Chord length | 7.0710678 m |
| Segment area (between chord and arc) | 7.1349541 m² |
| Angle | 90° = 1.5707963 rad |
| Share of the circle | 25% (circle area 78.539816 m²) |
Area 19.634954 m².
Multiply the circle’s area by the angle’s share: (θ/360) × πr². For θ = 60° and r = 10, that is 52.36.
A sector is bounded by two radii and an arc; a segment by a chord and an arc.
In radians the formulas become simple: area ½r²θ and arc rθ.