Model Train Scale Calculator

A model scale is a fixed ratio between a real-world size and its miniature equivalent. HO scale, for example, is 1:87.1 — meaning 1 inch on the model represents 87.1 inches (about 7.25 feet) in real life. Pick a scale and a direction, enter your measurement, and this calculator does the ratio math both ways.

How It Works

Model railroading scales are standardized so that track, locomotives, and buildings from different manufacturers stay compatible with each other. Each scale is written as a ratio — 1:87.1 for HO, 1:160 for N, and so on — meaning every inch of the model stands in for that many inches of the real thing. To go from real-world to model size, divide the real length by the ratio; to go the other way, multiply the model length by the ratio. The scale list here (Z, N, TT, HO, S, O, G) follows the ratios published in the NMRA's standard for scale and gauge, which is what most North American manufacturers build to — pick "Custom ratio" if you're working to a different national standard, like the slightly different HO and O ratios used in parts of Europe and Japan.

A Worked Example

Say you're scratch-building a 40-foot boxcar in HO scale. Convert 40 feet to inches: 40 × 12 = 480 inches. Divide by the HO ratio of 87.1: 480 ÷ 87.1 ≈ 5.51 inches — which matches the roughly 5.5-inch length HO modelers commonly cite for a 40-foot prototype boxcar. In centimeters, that's about 14.0 cm. Running the numbers the other way — entering 5.51 inches as a model measurement in HO scale — gives back 5.51 × 87.1 ≈ 480 inches, or exactly 40 feet, confirming the conversion holds in both directions.

Frequently Asked Questions

Why does N scale sometimes get listed as 1:148 instead of 1:160? British N scale traditionally uses 1:148 to keep the same track gauge readable with slightly larger, easier-to-detail models. This calculator uses 1:160, the NMRA/North American standard — use "Custom ratio" if you need 1:148.

Is HO really 1:87.1 and not just 1:87? Both are used informally, but 1:87.1 is the precise NMRA figure (it comes from dividing a foot into a number that works out evenly with 3.5mm-to-the-foot, the original British/European HO convention). The difference is small enough to ignore for anything under a few feet of prototype length.

What's a typical G scale ratio? 1:22.5 is the LGB-originated standard most G scale track and trains are built to, though "G" is used loosely across a range of roughly 1:20 to 1:32 depending on manufacturer — use "Custom ratio" if you know your line uses a different one.

Limits of This Calculator

This tool converts length only — it doesn't account for the visual "select-a-scale" tricks modelers use (like selective compression, where a building is shrunk beyond the true ratio to fit a smaller layout) or for a manufacturer building slightly off-ratio for practical reasons like wheel clearance. Different countries and eras have used more than one ratio for the same named scale, so always double-check the ratio your specific track system or model line actually uses before cutting material, and treat the result as a precise starting measurement rather than a substitute for test-fitting the real piece.