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.
- Radius R
- Arc angle θ
- Arc length s
- Chord c
- Height h
How it’s calculated
R = (c^2/4 + h^2)/(2h), arc = R theta, chord = 2R sin(theta/2), and height = R(1 - cos(theta/2)).
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.