Circular Sagitta, Chord & Radius Calculator

Method, example, and limits

Formula: R = c²/(8s) + s/2; central angle θ = 2 asin(c/(2R)); minor arc length = Rθ.

Inputs and units: c is chord length, s is sagitta measured perpendicular from the chord midpoint, and R is the circle radius. The angle is returned in degrees and arc length in the chord's unit.

Worked example: For a 100 mm chord and 10 mm sagitta, R = 130 mm, θ ≈ 45.2397°, and minor arc length ≈ 102.646 mm.

Result meaning: Radius and arc length describe the inferred circle segment; a small sagitta relative to the chord indicates a flatter, larger-radius arc.

Assumptions: The chord and sagitta describe a single circular arc, with positive lengths. The tool reports the minor central angle associated with that chord and radius.

Limits: This assumes a circular arc; it cannot determine whether a real object is truly circular. Shallow arcs are sensitive to sagitta measurement error because radius varies approximately with 1/s.