Curve Radius Calculator

Finding a Curve's Radius Without Ever Reaching Its Center

You can't run a tape measure to the center of a rail curve to find its radius — the center point is often buried underground or simply inaccessible. Track engineers solve this with the versine method: lay a chord across the curve, measure how far the rail bows away from that straight line at the midpoint, and the radius falls out of simple geometry.

The Formula

The chord is the straight-line length laid across the curve; the versine (or mid-ordinate offset) is the perpendicular distance from the midpoint of that chord to the rail. The second term is a small correction that matters more as the versine grows relative to the chord.

Where This Is Useful

• Track surveying — the versine method is a standard field technique for measuring curve radius without specialized surveying equipment.
• Speed limit setting — maximum safe speed through a curve is a direct function of its radius, so an accurate radius measurement is the starting point for setting or checking a speed restriction.
• Track maintenance — comparing measured versine values over time against the design radius helps detect track that has shifted out of alignment.

Worked Example

A smaller versine for the same chord length indicates a gentler (larger-radius) curve; a larger versine indicates a sharper curve.

How to Use This Calculator

1. Enter the Chord Length used for the measurement, in meters.
2. Enter the Versine (mid-ordinate offset) measured at the midpoint of that chord, in meters.
3. Select Calculate to get the curve radius.

Related Calculations

Curve radius and Track Gauge are both fundamental measurements checked during track surveys. For the speed implications of a sharper curve, see the Braking Distance Calculator.