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Model railway track for planning a layout
Ten practical tools for layout planning

Model Railway Calculators – Scale, Radius & Gradient

Calculate model dimensions, track curves, gradients, track helices, train and platform lengths, approximate space requirements and the required track length. All calculators work directly in your browser, without registration, on smartphones, tablets and computers.

Open calculators Planning guidance
From the first sketch to track construction

What can the model railway calculators calculate?

A convincing model railway layout begins with realistic dimensions. Even small calculation errors can mean that a train does not fit into a station, a gradient becomes too steep or a planned helix provides insufficient clearance. This page therefore combines the most important calculations for track plans, layout space, rolling stock and scenery in one interface.

The calculators support the commonly used Z, N, TT, H0, 00, S, 0, I and II scales, as well as H0e, H0m, H0f, 0e, 0m and IIm or G gauge. Scale ratios and model track gauges are considered separately. This is important because H0, H0e and H0m all use approximately the same 1:87 scale but run on tracks of different widths.

The results are intended as planning aids. Vehicle manufacturers may specify different minimum radii, long vehicles require more space on curves, and the possible gradient depends on the locomotive, train weight, traction tyres, radius and track condition. Before permanent construction, always carry out a practical test using the longest and heaviest trains you intend to operate.

Calculator 1 Compare scales Calculator 2 Radius and arc length Calculator 3 Calculate gradient Calculator 4 Plan a track helix Calculator 5 Determine train length Calculator 6 Size a platform Calculator 7 Prototype to model Calculator 8 Model to prototype Calculator 9 Estimate space requirements Calculator 10 Calculate track requirements
Enter values, calculate and use the result

Ten Calculators for Model Railway Planning

All results are automatically recalculated whenever an input field changes. The page does not use an external calculation library.

1

Scale Calculator and Gauge Comparison

Compare one prototype dimension across several model railway scales at the same time. This is useful for buildings, platforms, bridges, roads, trees and vehicle dimensions.

Gauge designation Scale Model dimension Typical model track gauge

Custom scale

Model dimension –
Conversion factor –
Planning guidance

Scale and track gauge are not the same thing. H0, H0e, H0m and H0f all use approximately 1:87 scale, but they represent different prototype gauges and use model tracks of different widths.

Calculation

Model dimension = prototype dimension ÷ scale ratio.

2

Radius Calculator for Model Railway Track

Calculates the diameter, circumference, arc length and a selectable reference value for the smallest curve radius.

Result

Diameter –
Arc length –
Full-circle circumference –
Track sections per full circle –
Reference radius –
–
Important for long vehicles

Overhang on the inside of a curve and outward swing on the outside require additional track spacing and more free space.

Calculation

Arc length = 2 × π × radius × curve angle ÷ 360.

3

Gradient Calculator for Model Railway Track

Calculates the percentage, per mille value, gradient angle and required route length for a specified height difference.

Result

Gradient –
Gradient in per mille –
Ratio –
Gradient angle –
Run at reference value –
–
A practical test remains important

Tight curves increase running resistance. A gradient that works on straight track may already be too steep on a tight curve.

Calculation

Gradient in percent = height difference ÷ horizontal run × 100.

4

Track Helix Calculator

Calculates total height, track length, gradient, clear height and the approximate outside diameter of a circular track helix.

Track helix result

Total height –
Total track length –
Gradient –
Clear height –
Outside diameter –
Track length per turn –
–
Allow more room for overhead lines and access

The clear height must account for vehicles, raised pantographs and the additional loading gauge required on curves. Additional access space is useful for maintenance and cleaning.

Calculation

The track length per turn is calculated as a three-dimensional helix using the circumference and the rise per turn.

5

Train Length Calculator

Calculates the length of a train using the locomotive, number of coaches or wagons, average vehicle length and a freely selectable allowance.

Result

Basic train length –
With allowance –
Prototype length –
For hidden yards and storage sidings

Measure vehicles over their couplings whenever possible. When several different vehicle types are used, adding their actual lengths is more accurate than using an average value.

Calculation

Train length = locomotive length + number of vehicles × average vehicle length.

6

Platform Length Calculator

Calculates the required usable platform length and the total length including safety allowances and ramps.

Result

Usable platform length –
Total length including ramps –
Prototype length –
Distinguish usable length from total length

The usable length is the section where passengers can board and leave a train. Ramps, stairs, entrances and tapered ends increase the total length of the complete structure.

Calculation

Total length = train length + allowances + ramps or end sections.

7

Prototype-to-Model Dimension Calculator

Converts real dimensions into the corresponding model size. Useful for buildings, roads, platforms, bridges and scratch-built details.

Model dimension

Millimetres –
Centimetres –
Metres –
Example

A prototype building measuring twelve metres is approximately 138 millimetres long in H0 before any deliberate compression for the layout is applied.

Calculation

Model dimension = real prototype dimension ÷ scale ratio.

8

Model-to-Prototype Dimension Calculator

Calculates the real-world size represented by an existing model dimension. This makes it easier to assess kits and scratch-built structures.

Prototype dimension

Metres –
Kilometres –
Millimetres –
Check whether buildings look realistic

Reverse calculation is particularly useful for stations and industrial buildings because it shows whether storey heights, doors, gates and building depths appear convincing.

Calculation

Prototype dimension = model dimension × scale ratio.

9

Space Requirements by Gauge

Estimates the length, depth and floor area of a simple layout shape using the radius, straight track length and safety margin.

Estimated space requirements

Layout length –
Layout depth –
Layout area –
Room including aisle –
–
Only an initial estimate

Turnout ladders, parallel tracks, buildings, hidden yards, access depth and the actual track geometry can substantially increase the required space.

Calculation

For an oval, the length and depth are calculated from two radii, the straight section and a safety margin on both sides.

10

Calculate Required Track Length

Adds straight track, two different curved sections, turnouts, track helix, hidden track and a material allowance.

Material requirements

Curve length 1 –
Curve length 2 –
Track length without allowance –
Track length with allowance –
Calculated flex-track sections –
Track bedding –
Do not count turnouts twice

When the turnouts are already included in the measured straight track length, set their calculation length to zero here.

Calculation

Total requirement = straights + curve lengths + turnouts + helix + hidden track + material allowance.

Interpreting the results correctly

What Should You Consider for Radius, Gradient and Train Length?

Calculators can reliably show geometric relationships. Operational reliability also depends on the vehicles, couplings, track system and layout construction.

Choose radii as large as possible

A technically passable minimum radius is not automatically visually convincing. Long passenger coaches swing out considerably, require greater track spacing and show clearly visible overhang on tight curves. Use the largest possible radius on visible main lines.

Do not start gradients abruptly

The transition from level track to a gradient requires a gentle vertical curve. A sharp change can cause long vehicles to ground, pull couplings apart or cause individual wheels to lose reliable contact with the rail.

Keep track helices accessible

A helix requires more than sufficient height for the vehicles. Your hands, cleaning tools and derailed vehicles must also remain accessible. Removable sections, side openings and monitored track sections make later operation easier.

Measure trains before planning

Manufacturer specifications may use different measuring points. The actual coupled train length is decisive for platforms and storage sidings. Place the longest planned train on straight track and measure it over the outer couplings.

Plan platforms with an allowance

A platform that exactly matches the train length requires exceptionally precise stopping. Additional room in front of and behind the train improves operational reliability. Signals, turnouts, clearance points and platform entrances may require further distances.

Include a material allowance

Flex track must be cut and cannot always be reused completely. Track bedding, cables and rail profiles also require an allowance. Complex turnout ladders and numerous curves justify a larger allowance than a simple route.

Distinguishing scale from model track gauge

Which Gauges Are Included in the Calculators?

The selection includes the most important European standard-gauge, narrow-gauge and garden-railway formats.

Designation Scale Model track gauge Typical use
Z 1:220 6.5 mm Very compact standard-gauge layouts and long routes
N 1:160 9 mm Compact layouts with long trains and large stations
TT 1:120 12 mm Balanced combination of space requirements and visible detail
H0 1:87 16.5 mm Largest selection of vehicles, track and accessories
H0m 1:87 12 mm Metre-gauge railways, RhB and Alpine narrow gauge
H0e 1:87 9 mm Narrow-gauge railways representing prototype gauges of around 750 to 800 mm
H0f / H0i 1:87 6.5 mm Field, industrial and very narrow light railways
00 1:76 16.5 mm Primarily British model railways
S 1:64 22.5 mm Larger scale that is less commonly used today
0 1:45 32 mm Highly detailed vehicles, modules and shunting layouts
0m 1:45 22.5 mm Metre-gauge railways in a large scale
0e 1:45 16.5 mm Narrow-gauge and light railways
I 1:32 45 mm Large vehicles and premium collector’s models
IIm / G usually 1:22.5 45 mm Metre-gauge and garden railways
II 1:22.5 64 mm Standard gauge in a very large scale
From the calculated result to the track plan

Suitable Tools and Track-Building Materials

After completing the calculations, track-planning software, flex track and track bedding can assist with practical implementation.

Märklin 60524 track-planning software on a USB drive
Digital layout planning

Märklin 60524 Track Planning 2D/3D

Planning software for several Märklin, Trix and LGB track systems with levels, gradients and three-dimensional display.

View product
Tillig 85125 H0 Elite flex track in a pack of ten
Custom track curves

Tillig 85125 H0 Elite Flex Track

Flexible track enables flowing radii, transition curves and routes beyond rigid track geometries.

View product
PIKO 55209 H0 A-Track flex track in a pack of ten
H0 track construction

PIKO 55209 A-Track Flex Track

The 940 mm flex track is suitable for custom straights, curves and generous transitions.

View product
NOCH 50410 cork track bedding for H0 gauge
Substructure and sound insulation

NOCH 50410 Cork Track Bedding

Flexible cork strips provide a clean base for H0 track without integrated roadbed and make later ballasting easier.

View product
Tracks and Turnouts Track Bedding and Cork Model Railway Guide Model Railways Märklin H0 Narrow-Gauge Railways H0m Gauge Garden Railways
Answers about layout planning

Frequently Asked Questions About the Model Railway Calculators

Key answers concerning scales, radii, gradients, track helices and layout space.

How do you convert a prototype dimension to H0?

Divide the prototype dimension by 87. A twelve-metre prototype therefore corresponds to approximately 137.9 millimetres in H0 scale.

What is the correct minimum radius for H0?

There is no universal minimum radius for H0. It depends on vehicle length, wheelbase, couplings, the track system and the intended use. The manufacturer’s specification for the individual vehicle remains decisive.

How is a model railway gradient calculated?

Divide the height difference by the horizontal route length and multiply the result by 100. A rise of 60 millimetres over a route length of 2,000 millimetres produces a gradient of three percent.

How much vertical rise should a helix have per turn?

The height must accommodate the vehicle, track, roadbed, any overhead line and a safety clearance. Together with the radius, it also determines the gradient. A greater rise per turn therefore usually requires a larger radius.

How long should a hidden-yard track be?

The track should be longer than the longest train you intend to operate. Also allow for stopping distance, stopping tolerance, isolated sections and a safety distance from the turnout.

Does a platform have to be as long as the entire train?

At a prototypical passenger station, the usable platform edge should at least accommodate the coaches intended for passengers. Deliberately shortened platforms are possible on small layouts, but they should suit the operating concept.

Why are H0, H0e and H0m the same size?

All three use 1:87 scale. The different designations represent different prototype track gauges and therefore use different model track gauges.

How much allowance should be included when buying track?

Around five to ten percent may be sufficient for simple routes. A larger material allowance is sensible when using many flex-track sections, curves, cuts and complex turnout ladders.

Is the calculated space requirement definitive?

No. The calculator provides an initial geometric estimate. Actual track geometry, turnouts, buildings, operator aisles, access depth and the substructure may significantly change the required area.

Can I use the calculators on a smartphone?

Yes. The input fields, results, tables and navigation adapt to narrow displays. The page only requires JavaScript to be enabled in the browser.

Calculated, Planned and Ready for Track Building

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