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Chord, arc & radius calculator

A radius you can't reach is measured from its chord: R = (c² + 4h²) / 8h. A 60 mm chord with a 5 mm height means a 92.5 mm radius — which is how you verify a large or partial radius with nothing but a scale or CMM points. The calculator also fits a circle through three measured points and converts between arc length, included angle, and radius.

Unit-agnostic geometry: enter any length unit consistently, and length results return in the same units.

Same arbitrary units throughout

Sagitta, in the same units

Enter all visible values to solve the geometry.

R = (c^2/4 + h^2)/(2h), arc = R theta, chord = 2R sin(theta/2), and height = R(1 - cos(theta/2)).

Triangle side and angle solving: Triangle solver.

Derived

Derived from circular segment formulas and the circumcenter determinant formula for three points

Values follow the governing standard, which is authoritative for production and inspection decisions. Verify against it before you rely on a number.

Standard names are trademarks of their respective owners; ASdrawn is not affiliated with or endorsed by any standards body.

How do you measure a radius you can't reach?

A large or partial radius — a blend, a segment, an arc with no accessible centre — cannot be measured with a radius gauge. Instead you measure a chord across it and the height (sagitta) at the chord’s midpoint, and the radius follows from R = (c² + 4h²) / 8h. Three points measured on the arc give the same answer through the circle-through-three-points fit.

Use it to verify a radius on a CMM or with gauge blocks and a height stand, to reconstruct a worn or partial feature, or to convert between arc length, included angle, chord, and height when a drawing dimensions one and the setup needs another.