WoodCalcs.uk
Radius Calculator — Find Radius from Chord & Height
Find radius from chord and height measurements for curved woodworking pieces.
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
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.
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.
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.
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.
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Last updated: February 2026
All calculations are estimates. Always verify measurements and material quantities before cutting or purchasing.