Track Superelevation Calculator

Calculate rail cant (superelevation) from curve radius and design speed using the AREMA formula e = 0.0007 × D × V².

Inputs

Design speed

mph

Curve radius

Max actual cant

Max cant deficiency

Tab to move between fields

Results

Equilibrium cant

7.22 in

≈ 2 credit cards

Applied cant6 in

Cant deficiency1.22 in

Deficiency within limit1

Degree of curve2.86°

Max safe speed67 mph

Spiral run-off length186 ft

Lateral acceleration0.06 g

How to Use This Calculator

Enter Design speed, Curve radius, and Max actual cant.
Set Max cant deficiency.
Review the Equilibrium cant (in) result.
Use Applied cant (in) and Cant deficiency (in) to inform your decision.

How the result changes with Design speed

Design speed	Equilibrium cant
25	1.25 in
73	10.69 in
132	34.94 in
181	65.7 in

What each input means

Design speed: Maximum operating speed through the curve.
Curve radius: Radius of the horizontal curve in feet.
Max actual cant: Maximum allowed superelevation (6 in freight, 8 in passenger per AREMA).
Max cant deficiency: Maximum allowed unbalanced superelevation (typically 3 in for freight).

What each result means

Equilibrium cant: Theoretical superelevation for zero lateral force at design speed.
Applied cant: Actual superelevation limited by the maximum allowed.
Cant deficiency: Unbalanced superelevation (equilibrium minus actual).
Deficiency within limit: 1 = within limit, 0 = exceeds maximum allowed cant deficiency.
Degree of curve: Standard chord definition: D = 5729.578 / R.
Max safe speed: Maximum speed for the given actual cant plus maximum unbalanced.
Spiral run-off length: Minimum transition length to ramp from zero to full cant (AREMA).
Lateral acceleration: Uncompensated lateral acceleration experienced by passengers/freight.

How this is calculated

Worked example, using the default values

Identify Input Parameters
4 parameters
Design speed = 60, Curve radius = 2000, Max actual cant = 6, Max cant deficiency = 3 = 4 input(s) provided
Calculate Equilibrium cant
Equilibrium cant = 0.0007 * degreeOfCurve * speedMph * speedMph
7.219 = 7.219
Calculate Applied cant
Applied cant = min(equilibriumCant, maxCantIn)
6 = 6
Calculate Cant deficiency
Cant deficiency = equilibriumCant - actualCant
1.219 = 1.219

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