Train Braking Distance Calculator

Work out train braking distance instantly with clear inputs, formula shown and shareable results.

About Train Braking Distance Calculator

Braking distance is v squared divided by twice the deceleration, plus the distance covered during brake build-up. A falling gradient subtracts g times the gradient from the available deceleration, which is why descending grades lengthen stopping distance sharply and drive signal spacing on mountain lines.

Formula

Braking distance

d = v x t_buildup + v^2 / (2 x (a - g x gradient))

Worked example

With the default values below, Train Braking Distance Calculator returns Total stopping distance of 1,142. Change any input above and every figure here is recalculated in your browser.

Inputs used

Train speed: 120 km/h
Braking deceleration: 0.6 m/s²
Driver and brake build-up delay: 4 s
Gradient (down positive): 0.5 %

Results

Total stopping distance: 1,142 m
Pure braking distance: 1,008 m
Distance during build-up: 133 m
Time to stop: 64.50 s

Step by step

1Values used
2Braking distance
3Total stopping distance= 1,142 m
4Pure braking distance= 1,008 m
5Distance during build-up= 133 m
6Time to stop= 64.50 s

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, 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 is brake build-up so important?

Air brakes propagate along the train, so a long freight train can take 10-20 seconds to reach full braking, covering hundreds of metres at line speed.

What decelerations are realistic?

Roughly 0.4-0.6 m/s2 for loaded freight, 0.8-1.2 m/s2 for passenger stock in service braking and up to 1.5 m/s2 in emergency.