Curve Radius Calculator
Description
This curve radius calculator finds a model railroad curve's exact radius without needing its center point — useful any time you hand-bend flex track, or shape a curve against benchwork or a wall, where there's no way to reach the true center to swing a trammel and measure the radius directly. Instead, it works from just two measurements you can take with a straightedge and a ruler.
Lay a straightedge across two points on the curve to form a chord — a straight line connecting them — and measure its length. Then, at the chord's midpoint, measure straight across (at a right angle to the chord) to the curve itself — that distance is the middle ordinate. Enter both below and this calculator returns the curve's radius, so you can check it against your intended radius or a minimum-radius requirement without ever finding the center point.
Sources
- Standard surveying chord/middle-ordinate circle relations (chord = 2R·sin(θ/2), middle ordinate = R·(1 − cos(θ/2))), combined into the closed-form radius formula R = C²/(8M) + M/2 used here — this relation and its 200 ft chord / 5 ft middle-ordinate worked example (R = 1,002.5 ft) appear consistently across civil engineering and surveying references.
Disclaimer: accuracy depends on how precisely you measure the chord and middle ordinate — use the longest chord practical for your curve, and measure the middle ordinate exactly at the chord's midpoint, for the best result.