Circle sector calculator
Enter the radius and the central angle and get the area of the sector, together with the arc length and the perimeter of the sector.
Fill in the fields; the answer appears here straight away.
How it's worked out
How it works
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Enter the values
Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.
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Instant answer
The answer appears as you type, with the most important intermediate values.
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See the working
Under "How it's worked out" you see the steps, handy for checking your own calculation.
The formula
A sector is a fraction of the whole circle, whose area is πr². So sector area = (angle ÷ 360°) × πr², or ½r²θ with the angle θ in radians.
For a radius of 10 and an angle of 60°: (60 ÷ 360) × π × 10² = 52.36.
Perimeter of the sector
The edge of a sector is the arc plus two radii: (angle ÷ 360°) × 2πr + 2r. Only need the curved part? Use the arc length calculator.
Worked example: a pizza slice
A pizza of 16 cm radius is cut in 8 equal slices, so each has a central angle of 45°. The area of a slice is (45 ÷ 360) × π × 16² ≈ 100.5 cm². The crust edge of a slice is (45 ÷ 360) × 2π × 16 ≈ 12.57 cm, and the perimeter of the slice adds the two cut edges of 16 cm each, about 44.57 cm.
Fractions of a circle
| Share of the circle | Central angle |
|---|---|
| 1/8 | 45° |
| 1/6 | 60° |
| 1/4 | 90° |
| 1/3 | 120° |
| 1/2 | 180° |
The sector area is that fraction of the circle's area πr². The default example (radius 10, 72°) is one fifth of a circle: 62.83, which is a fifth of the circle area 314.16.
Related measurements
For only the curved edge, use the arc length calculator. To convert between a share and an angle, use the percentage calculator.
Frequently asked questions
How do I find the area of a sector from the arc length?
Use A = ½ · r · s, with s the arc length. For r = 10 and s = 12.566, that is ½ × 10 × 12.566 = 62.83.
What is the difference between a sector and a segment?
A sector is the slice between two radii and the arc, like a slice of pizza. A segment is the part between the arc and the straight chord. This calculator gives the sector and shows the chord length.
Which angle do I enter?
The central angle, measured at the middle of the circle, between 0° and 360°. A sector of 25% of the circle has an angle of 90°.
Can I use radians?
Yes, choose radians above the fields. In radians the area is ½ r² θ and the arc is r θ.