Circle Sector Calculator
Find the area, arc length, perimeter and chord of a circle sector from the radius and angle, the arc length or the sector area.
A circle sector is the pie-slice region between two radii and the arc that joins them. Give this calculator the radius and central angle, or one of the other supported pairs, and it returns the sector area, arc length, perimeter and the straight chord across the opening. It is useful for pizza portions, curved garden beds, pie-chart slices and geometry homework.
How to use this tool
- Choose which two measurements you already know.
- Enter the radius, plus the central angle, arc length or sector area as required.
- Pick degrees or radians for the angle.
- Read the area, arc length, perimeter and chord; the share of the full circle shows how big the slice is.
Formula
A = ½ r² θ s = r θ P = 2r + s (C for a full circle) c = 2r sin(θ / 2)
θ is the central angle in radians (degrees × π / 180), r is the radius, s the arc length, P the perimeter of the slice and c the chord. In degrees the area formula is the same thing written as A = (θ / 360) × π r²: the sector is that fraction of the whole circle.
Example
A slice with radius 10 cm and a 60° angle: θ = 60 × π / 180 ≈ 1.0472 rad. The area is ½ × 10² × 1.0472 ≈ 52.36 cm², the arc length is 10 × 1.0472 ≈ 10.47 cm, the perimeter is 20 + 10.47 ≈ 30.47 cm, and the chord is 2 × 10 × sin 30° = 10 cm. The slice is 16.67% of the circle.
Frequently asked questions
How do I find the area of a sector in degrees?
Divide the angle by 360 and multiply by the area of the whole circle: A = (θ / 360) × π r². For a 90° sector with radius 4 that is ¼ × π × 16 ≈ 12.57 square units.
What is the difference between arc length and chord length?
The arc follows the curved edge of the circle, while the chord is the straight line between the two ends of the arc. The chord is always the shorter of the two for any angle above zero.
Can I find the angle from the arc length?
Yes. Choose “Radius and arc length”: the angle in radians is θ = s / r. An arc of 2π with radius 4 gives θ = π/2, which is 90°.
What is the difference between a sector and a segment?
A sector is bounded by two radii and an arc, like a pie slice. A segment is bounded by a chord and an arc; its area is the sector minus the triangle formed by the two radii and the chord.
Last updated: 2026-10-30