Circle Sector, Arc and Chord Calculator for Angles, Lengths and Areas

Updated October 13, 2026By Unit Conversion Plus

Solve the measurements of a circular sector and segment from two known values.

Known measurements

Arc = rθ · Chord = 2r sin(θ/2) · Sector area = r²θ/2

The angle θ must be in radians in these formulas. The segment area is the sector area minus the triangle formed by the two radii and chord.

Sagitta is the maximum perpendicular distance between a chord and its arc. It equals r(1 − cos(θ/2)) for a minor arc.

What is the difference between an arc and a chord?

An arc follows the curved circle; a chord is the straight line joining its endpoints.

Can the central angle exceed 180°?

Yes when entered directly or from arc length, up to 360°. Chord and sagitta inputs describe the minor sector up to 180°.