Circle Calculator
Circle from radius, diameter, circumference or area, then chord, arc length, sagitta, sector and segment area from an angle, chord, arc or sagitta.
Radius, diameter, circumference and area, and for the arc: central angle in degrees and radians, chord, arc length, sagitta, apothem, sector area, segment area and sector perimeter.
Example: Radius 10 with a 60° central angle: chord 10, arc 10.47, sagitta 1.34, sector 52.36, segment 9.06; a chord of 12 with sagitta 2 on the same circle spans 73.74°.
Everything follows
from the radius.
The circle identities, how a chord, arc or sagitta gives the central angle, and the segment and sector formulas.
The circle
Radius, diameter (2r), circumference (2πr) and area (πr²) are four spellings of one number; enter any of them and the other three follow, with π to double precision.
Chord, arc, sagitta
A central angle θ (radians) cuts a chord c = 2r·sin(θ/2), an arc of length rθ, and a segment whose height — the sagitta — is s = r(1 − cos θ/2); the apothem r − s is the distance from the centre to the chord. Going the other way: from a chord θ = 2·asin(c/2r), from a sagitta θ = 2·acos(1 − s/r), from an arc θ = L/r. A chord alone is ambiguous (two arcs), so the page gives the minor arc and says so.
Sector and segment
The sector (pizza slice) has area ½r²θ and perimeter rθ + 2r; the segment (the part cut off by the chord) has area ½r²(θ − sin θ). Units are whatever you entered, squared for areas; angles are shown in both degrees and radians. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- C = 2πr, A = πr²; chord 2r·sin(θ/2), arc rθ, sagitta r(1 − cos θ/2), sector ½r²θ, segment ½r²(θ − sin θ); θ from chord 2·asin(c/2r), from sagitta 2·acos(1 − s/r)
Last reviewed 21 September 2026. How results are checked: How we verify.