Find the arc length, sector area, and segment area of a circle — free and instant.
A sector is the pie-slice-shaped region between two radii and the arc they cut off; a segment is the smaller region between a chord and the arc, after cutting the triangular part of the sector away. Given a radius and the angle at the center, this finds arc length, sector area, segment area, and the chord length (the straight-line distance across the segment, connecting the two ends of the arc).
Sector area scales the full circle's area (πr²) by the fraction of the full 360° the angle represents. Segment area is the sector area minus the area of the triangle formed by the two radii and the chord, computed using ½r²sin(θ). Chord length comes from 2r×sin(θ/2) — at exactly 60°, this always equals the radius itself, since the two radii and the chord form an equilateral triangle.
Every measurement here is editable, and any two of the six can be the ones you know — enter, say, a radius and a target sector area, and this solves for the angle that produces it; or an angle and a sector area, and it solves for radius instead. Whichever two fields you've most recently changed become the "known" pair, and the other four update to match them.
The sector becomes the entire circle, and the segment area equals the full circle’s area too, since there’s no triangular part to subtract at a full turn.
The triangular part of the sector isn’t a simple fraction of the circle — its area depends on the actual geometry of two radii meeting at that angle, which is exactly what ½r²sin(θ) captures.
This tool expects degrees — convert radians to degrees first (multiply by 180/π) if that’s what you have.
The chord is the straight-line distance directly across the segment, connecting the two endpoints of the arc. The arc length is the curved distance along the circle between those same two points — always longer than the chord, except at very small angles where they’re nearly equal.
Whichever two fields you’ve most recently edited become the known pair — the other four (including radius and angle themselves) are recalculated to be consistent with those two.
This tool tells you directly rather than showing a wrong or nonsensical answer — for example, a sector area larger than what any angle up to 360° could produce at that radius.