How do I find the radius of a curve from a chord?

Measure the chord (straight line between the two ends of the arc) and the sagitta (the height from the midpoint of the chord to the highest point of the arc). Then use the formula: Radius = chord² / (8 x height) + height/2 — keep the height in the denominator. For example, a 600 mm chord with a 50 mm sagitta gives 600² / (8 x 50) + 50/2 = 900 + 25 = 925 mm. This calculator does the maths for you.

What is a sagitta in woodworking?

The sagitta (also called the rise or height) is the perpendicular distance from the midpoint of a chord to the arc. If you lay a straightedge across a curved piece, the sagitta is the gap between the straightedge and the apex of the curve.

How do I draw a large radius arc in the workshop?

For radii up to about 2 metres, use a trammel (a beam compass) made from a strip of MDF with a nail at one end and pencil at the other. For very large radii, use the three-point method: calculate the sagitta, mark three points, and spring a thin batten through them.

How do I find the radius of an existing curved piece?

Place a straightedge across the curve and measure the chord length and the gap (sagitta) at the centre. Enter these into this calculator to find the radius. For a full circle, simply measure the diameter and divide by 2.

WoodCalcs

Radius Calculator — Find Radius from Chord & Height

Find radius from chord and height measurements for curved woodworking pieces.

Calculation MethodChord & height: one straightedge across the curve. 3 offsets: three equally spaced batten measurements

Chord Length

Straight-line distance between arc ends

Sagitta (Height)

Rise from chord midpoint to arc

How We Calculate This

This calculator finds the radius of a circle from chord and sagitta (height) measurements.

The formula

Radius = (c² / (8 x h)) + (h / 2)

Where c = chord length and h = sagitta (height from chord midpoint to arc).

The arc length is calculated as: Arc = Radius x Central angle (radians)

Central angle = 2 x arccos((Radius − sagitta) / Radius). This range-safe form stays correct for deep arcs where the sagitta exceeds the half-chord (central angle > 180°), unlike the half-chord arcsin form which breaks down past a semicircle.

Frequently Asked Questions

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Last updated: February 2026

All calculations are estimates. Always verify measurements and material quantities before cutting or purchasing.