Curve Radius from Chord Calculator

About this calculator

This calculator finds the radius of a circular curve from two field measurements: the chord length (a straight line between two points on the curve) and the mid-ordinate or offset (the perpendicular distance from the chord's midpoint to the curve). The formula, derived from the geometry of a circle, is R = C²⁄8m + m⁄2, where C is the chord and m is the mid-ordinate.

It's a classic technique in surveying, used to lay out horizontal curves on roads and railways and to reconstruct the radius of an existing curve from a handful of tape measurements, without needing to locate the curve's actual center point.