Why does weight scale by the cube?

Weight (mass) depends on volume, which is a three-dimensional quantity. If you shrink all three dimensions by the scale factor, volume shrinks by the scale factor cubed. A 1:72 model has 1/72 the length, 1/72 the width, and 1/72 the height, so its volume (and thus weight, assuming same density) is 1/(72x72x72) = 1/373,248th of the original.

Will my model actually weigh this much?

No — this is the theoretical weight if the model were made of the same material as the real object. A real tank is made of steel, but a plastic model uses much lighter polystyrene. This calculation is mainly useful for understanding scale physics or for ballasting model railway wagons to realistic scale weights.

How is this useful for model railways?

Railway modellers sometimes ballast wagons to scale weight for more realistic running. The NMRA recommends a base weight plus additional weight per unit length. This calculator tells you what the prototype wagon weighs at scale, helping you decide on ballasting.

ModelCalcs

Scale Weight Calculator — Cube Law Weight

Calculate the theoretical scale-equivalent weight of an object using the cube law. Weight scales by the cube of the scale factor.

Real-World Weight

Weight Unit

Scale

How We Calculate This

Weight (assuming same material density) scales with the cube of the scale factor.

Formula

Scale weight = Real weight ÷ Scale³

Example: A real 40-tonne tank at 1:72 scale:
40,000 kg ÷ 72³ = 40,000 ÷ 373,248 = 0.107 kg = 107 grams.
(A plastic kit would weigh far less since polystyrene is much lighter than steel.)

Frequently Asked Questions

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Last updated: February 2026

All calculations are estimates. Always verify quantities before purchasing materials.