Curve Radius from Chord Calculator

How it is calculated

The tool uses the exact chord-and-sagitta relation of a circle: R = C² / (8 × m) + m / 2. C is the length of the straight chord between two points on the curve and m is the mid-ordinate (offset), the perpendicular distance from the middle of the chord to the arc. Both must be greater than zero and in the same unit; the radius comes out in that unit with two decimals. For a shallow curve the second term m/2 is small, but it is included, so the answer is not the common approximation R ≈ C²/8m. The tool assumes a single circular arc and cannot detect a measuring error or a curve that is not circular.

Common mistakes

• Mixing units, such as a chord in metres and an offset in centimetres. Convert both to the same unit first; the radius is returned in that unit.
• Measuring the offset from the end of the chord instead of from its midpoint. The formula needs the perpendicular distance at the middle.
• Using a very short chord with a tape reading error. When the offset is only a few millimetres, a 1 mm error changes the radius a lot, so use a longer chord.
• Entering the central angle or the arc length in place of the chord; the tool needs the straight-line distance between the two points.
• Assuming the curve is a perfect circle. Spiral transition curves have changing radius, so one chord gives only the local radius.