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Transition Curve Length Calculator

Work out transition curve length instantly with clear inputs, formula shown and shareable results.

About Transition Curve Length Calculator

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.

Formulas

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

Worked example

With the default values below, Transition Curve Length Calculator returns Transition length to adopt of 121.93. Change any input above and every figure here is recalculated in your browser.

Inputs used

Design speedminimum 10 km/h
80 km/h
Circular curve radiusminimum 10 m
300 m
Rate of change of centrifugal accelerationminimum 0.05 m/s³
0.3 m/s³
Superelevation rateaccepts 1–12 %
7 %

Results

Transition length to adopt
121.93 m
Length from rate of change of acceleration
121.93 m
Length from the empirical formula
57.60 m
Length from superelevation run-off
49.00 m

Step by step

  1. 1Values used
  2. 2Rate of change
  3. 3Empirical
  4. 4Superelevation run-off
  5. 5Transition length to adopt= 121.93 m
  6. 6Length from rate of change of acceleration= 121.93 m
  7. 7Length from the empirical formula= 57.60 m
  8. 8Length from superelevation run-off= 49.00 m

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
  • Preliminary estimate only. Transition curve design must follow the geometric design standard adopted by the road authority.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Preliminary estimate only. Transition curve design must follow the geometric design standard adopted by the road authority.

Frequently Asked Questions

How is the Transition Curve Length figure worked out?

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.

Why does a transition curve matter?

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.

What values do I need to enter?

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.

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