What this calculator does
When a train runs through a curve, centrifugal acceleration pushes it toward the outside rail. Track engineers counter this by raising the outer rail — applying cant (also called superelevation or crosslevel). This calculator takes your design speed, curve radius and applied cant and returns the three numbers every curve review needs: equilibrium cant, cant deficiency, and cant excess.
The formula
Equilibrium cant is the cant at which the resultant of gravity and centrifugal force acts perpendicular to the plane of the rails — the passenger feels no sideways push:
E_eq = (G_eff × V²) / (127 × R)
where E_eq is equilibrium cant in millimetres, G_eff is the effective gauge in millimetres (the spacing between rail-head centres, about 1500 mm for standard-gauge track), V is speed in km/h and R is curve radius in metres. For standard gauge this collapses to the familiar rule of thumb E ≈ 11.8 × V² / R.
Cant deficiency is the shortfall between equilibrium cant at line speed and the cant actually installed. Cant excess is the opposite check, run at the speed of the slowest regular traffic: how much more cant is installed than that traffic needs.
Why you can’t just install equilibrium cant
Real curves carry mixed traffic. If you cant the curve perfectly for a 115 km/h passenger service, a 60 km/h loaded coal train on the same curve runs with large cant excess — it leans on the low rail, accelerating low-rail head wear, gauge-corner fatigue and track geometry deterioration. Design cant is always a compromise, which is why standards set limits on both deficiency (passenger comfort, vehicle safety) and excess (low-rail loading, wheel unloading in wind).
Typical limits
Every network sets its own values, but common ranges for conventional rolling stock on plain track are: applied cant up to about 150 mm on passenger-dominant track (often 110 mm or less where heavy freight dominates), cant deficiency in the 75–110 mm range, and cant excess up to about 100–110 mm. Tilting or approved higher-deficiency stock can run beyond this. Always confirm against the standard that applies to your network — for example RISSB AS 7635 (Australia), TfNSW ESC 210 (NSW), or EN 13803 (Europe).
Worked example
A 900 m radius curve carries passenger services at 115 km/h and loaded freight at 60 km/h, with 95 mm applied cant. Equilibrium cant at 115 km/h is 1500 × 115² / (127 × 900) ≈ 173.5 mm, so deficiency is 173.5 − 95 ≈ 78.5 mm — acceptable on many networks but worth checking against the applicable standard. At 60 km/h equilibrium cant is ≈ 47.2 mm, so the freight sees ≈ 47.8 mm of excess — comfortably inside typical limits.
FAQ
What’s the difference between cant and superelevation? None — they’re the same quantity. “Cant” is common in UK/Australian practice, “superelevation” in North America (where it’s usually quoted in inches).
Why 127 in the denominator?
It’s the constant that falls out of g and the unit conversions: 127 ≈ 3.6² × 9.81, letting you use km/h, metres and millimetres directly.
Does this handle transition curves? This tool covers circular curve equilibrium. Cant gradient, rate of change of cant and rate of change of deficiency through transitions are separate checks — a transition length calculator is on the roadmap.
This tool provides indicative figures for preliminary design and checking. Final designs must be verified against the standards and rolling-stock approvals applicable to your network.