TOOLS / LAYOUT

Chord, arc and sagitta calculator

From a radius and an angle — or a radius and a chord — get the chord length, arc length, sagitta and segment area for marking an arc on plate or checking a curved panel.

Chord length500.00 mm

Central angle: 60.00° · Arc length: 523.60 mm · Sagitta: 66.99 mm · Segment area: 22647 mm².

Pure circle geometry for marking arcs and checking curved panels. Confirm the radius and angle against the drawing; a small radius error changes the sagitta quickly on shallow arcs.

Formula

Chord = 2R·sin(θ/2). Arc length = R·θ, with θ in radians. Sagitta = R·(1 − cos(θ/2)). Segment area = (R²/2)·(θ − sin θ). From radius and chord, the central angle is θ = 2·asin(chord ÷ 2R), and the same formulas follow.

Standard / source

Standard circle geometry, as used in sheet-metal layout and pipefitting (chord = 2R·sin(A/2) is the standard fitting-layout form). No code table is involved; accuracy depends on the radius and angle measured on the job.

Worked example

Radius 500 mm, central angle 60°: chord = 2 × 500 × sin 30° = 500.00 mm; arc = 500 × π/3 = 523.60 mm; sagitta = 500 × (1 − cos 30°) = 66.99 mm; segment area = (500²/2) × (1.0472 − 0.8660) = 22,647 mm². These are the calculator's default inputs, so it shows these values on load.

Safety note

Layout geometry only. For pressure-piping arcs and bends, geometry alone does not approve the fitting — code design and inspection govern.