Work out transition curve length instantly with clear inputs, formula shown and shareable results.
Transition curve length is checked three ways and the longest governs: the rate of change of centrifugal acceleration, V³ / (C R) with speed in metres per second; the empirical 2.7 V² / R with speed in kilometres per hour; and the length needed to run off the superelevation at an acceptable rate, commonly one in two hundred.
Rate of change
L = V³ / (C R), V in m/s and C typically 0.3 to 0.6 m/s³
Empirical
L = 2.7 V² / R with V in km/h
Superelevation run-off
L = crossfall x lane width / permitted run-off gradient
Preliminary estimate only. Transition curve design must follow the geometric design standard adopted by the road authority.
L = V³ / (C R), V in m/s and C typically 0.3 to 0.6 m/s³. Transition curve length is checked three ways and the longest governs: the rate of change of centrifugal acceleration, V³ / (C R) with speed in metres per second; the empirical 2.7 V² / R with speed in kilometres per hour; and the length needed to run off the superelevation at an acceptable rate, commonly one in two hundred.
It introduces curvature gradually so the steering input and lateral acceleration build smoothly, and it provides the length over which superelevation can be developed without an abrupt twist in the carriageway.
This calculator takes 4 inputs: Design speed, Circular curve radius, Rate of change of centrifugal acceleration, Superelevation rate. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.