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Randozi
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Model Railway Track Geometry

Plan the shape of your track: the grade of a ramp, the length a ramp needs, the length of rail in a curve and the height a helix gains per turn, all in millimetres.

Grade

2 %

20 ‰
Height exaggerated 7× so that the slope can be seen.

Geometry only: it does not say what grade a locomotive can climb or which radius your rolling stock accepts. Test on a short piece of track.

How it works

  1. Choose the calculation: grade, ramp length, curve arc or helix rise.
  2. Enter the values in millimetres (the radius is measured at the centre of the track).
  3. Read the result and the diagram where there is one.
  4. Copy the result into your plan, and test it on a piece of track before you build.

What people use it for

  • Checking a ramp

    20 mm of rise over 1,000 mm is a 2 % grade: check a ramp before you cut the board.

  • Fitting a bridge or a tunnel

    Find the horizontal length you need to climb a given height at the grade you choose.

  • Buying curved track and planning a helix

    Get the arc length of a curve, or how much height a turn of a helix gains.

Questions

What are the formulas?
Grade % = 100 × rise ÷ run. Ramp run = 100 × rise ÷ grade %. Arc = π × radius × angle ÷ 180. Rise per helix turn = 2π × radius × grade % ÷ 100. A grade of 2 % over 1,000 mm climbs 20 mm.
Does it say which grade my locomotive can climb?
No. The tool only does the geometry. What a locomotive can pull depends on its weight, its traction and the train, so test your own on a short ramp.
Which radius should I enter for a curve?
The radius to the centre line of the track. It is not a minimum allowed radius: check what your locomotives and wagons accept.
What does the helix rise leave out?
Only the height gained per turn. The clearance for the tallest vehicle, the thickness of the track bed and the supports come on top of it, and they are yours to measure.