Circular Sector Calculator
The area and arc length of a circular sector from radius and angle.
Result
Sector area
19.63
Arc length
7.85
How it works
A sector is a pizza slice of a circle: the region between two radii and the arc joining them. Its share of the whole circle equals its share of the full turn, so the area is (angle/360) × π·r² and the arc length is (angle/360) × 2π·r. A quarter circle (90°) therefore takes exactly a quarter of the area; a 60° slice takes a sixth. With r = 10 and a 90° angle, the area is 78.5 and the arc 15.7. Sectors turn up wherever circles get shared or swept: pie-chart wedges (each category's percentage times 360 gives its angle), a windscreen wiper's swept zone, an irrigation arm's covered field, or the fabric needed for a flared skirt panel.
Advertisement
Frequently asked questions
What is a sector?
The region between two radii and the arc between them — a slice of pie.
What is the arc length?
The curved edge of the sector, a fraction of the full circumference.
How do I turn a percentage into a pie-chart angle?
Multiply the share by 360°. A 25% category takes 90°, 10% takes 36°. This calculator then gives that wedge's exact area and arc for any radius.
Advertisement