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Register nowPlanning a ramp on your model-railway layout? Calculate the gradient in per-mille (‰) from height and length — or the other way around.
Enter rise and run.
How much height does the track climb for a given gradient and length?
How much track do you need to climb a given height at a given gradient?
Gradients bring a layout to life: ramps connect different levels and make tunnels and bridges possible. But sections that are too steep overload locomotives — especially with long trains.
Gradient in per-mille indicates how many millimetres of rise occur over 1000 mm of track length. A gradient of 20 ‰ means: for every metre of track the train climbs 20 mm.
| Gradient | Rating | Suitability |
|---|---|---|
| up to 10 ‰ | Very gentle | Suitable for all trains and lengths |
| 10–20 ‰ | Normal | Well suited; short trains no problem |
| 20–30 ‰ | Steep | Short trains, powerful locos required |
| 30–40 ‰ | Very steep | Only for single locos or short consists |
| over 40 ‰ | Extreme | Not recommended — rack railways only |
As a rule of thumb: 20–30 ‰ at most (2–3 %). At steeper gradients the tractive effort of the locomotive drops sharply. You should also plan a sufficient transition length at the start of the incline so couplings do not open.
At 20 ‰, climbing 100 mm requires 5000 mm (5 m) of track. The gradient calculator above computes this automatically for any values.
In model-railway planning, the track length (along the rail) is normally used. At the gradients common in model railways, the difference from the horizontal distance is negligible.