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Track Curvature Radius Calculator

Work out track curvature radius instantly with clear inputs, formula shown and shareable results.

About Track Curvature Radius Calculator

Radius is found from a chord and its versine: R = chord squared divided by eight times the versine. That is the basis of track measurement in the field. From the radius and speed follow the lateral acceleration and the equilibrium cant that would balance it.

Formula

Versine method

R = C^2 / (8 x versine); equilibrium cant = 1500 x V^2 / (R x g) mm for 1435 mm gauge

Worked example

With the default values below, Track Curvature Radius Calculator returns Curve radius of 961.5. Change any input above and every figure here is recalculated in your browser.

Inputs used

Chord length measured
20 m
Versine (mid-ordinate)
0.052 m
Line speed
90 km/h

Results

Curve radius
961.5 m
Degree of curve (100 ft chord)
1.82 °
Uncompensated lateral acceleration
0.65 m/s²
Equilibrium cant
99 mm

Step by step

  1. 1Values used
  2. 2Versine method
  3. 3Curve radius= 961.5 m
  4. 4Degree of curve (100 ft chord)= 1.82 °
  5. 5Uncompensated lateral acceleration= 0.65 m/s²
  6. 6Equilibrium cant= 99 mm

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, 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.
  • Rail results are planning estimates only. Verify against the infrastructure manager's rule book, approved braking curves and applicable railway safety regulations.

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

Rail results are planning estimates only. Verify against the infrastructure manager's rule book, approved braking curves and applicable railway safety regulations.

Frequently Asked Questions

Why measure versine rather than radius?

A chord and its mid-offset can be measured directly on the rail with a string line, while the radius cannot. Versine is also what track recording cars record.

What is degree of curve?

The North American measure: the central angle subtended by a 100 ft chord. It is roughly 1746 divided by the radius in metres.

Related Calculators

Track Curvature Radius Calculator – Calculate Curve radius