Last reviewed: 15 October 2026. Formulas, unit factors and the standards table below were checked against the sources listed on this page.
The formulas
A scale of 1:N means one unit on the model equals N units in reality.
- Model size = real size ÷ N. Example: a 7.2 m aircraft at 1:72 is 10 cm long.
- Real size = model size × N.
- From scale 1:A to scale 1:B: multiply by A ÷ B. Example: 1:72 to 1:48 is × 1.5.
- Scale factor = scaled size ÷ original size. Area changes with the factor squared, volume with the factor cubed.
- Map distance: real distance = map distance × N (1 cm on a 1:25000 map is 250 m).
- Miniature figures: ratio = real height ÷ figure height, based on a 1.8 m person.
Units
All conversions go through millimetres with exact factors: 1 cm = 10 mm, 1 m = 1000 mm, 1 inch = 25.4 mm and 1 foot = 304.8 mm (the international inch and foot, NIST). Imperial architect scales follow from these: ¼″ = 1′ means 0.25 inch for 12 inches, so 1:48.
Rounding
Results are calculated at full precision and only rounded for display: up to four decimals below 1, three decimals below 100 and two decimals above; trailing zeros after the decimal point are removed. Very small or very large values are shown in scientific notation. Reference tables on the scale pages show whole numbers from 100, one decimal from 10, two decimals from 1 and three decimals below 1.
Scale standards
Model railroad ratios follow the published standards of the NMRA (North America) and the NEM standards of MOROP (Europe). Where they differ, both are shown.
| Gauge | Ratio | Track gauge |
|---|---|---|
| HO | 1:87.1 (NMRA) · 1:87 (NEM, "H0") | 16.5 mm |
| OO | 1:76.2 (4 mm to the foot) | 16.5 mm |
| N | 1:160 (Japanese N mostly 1:150) | 9 mm |
| TT | 1:120 | 12 mm |
| Z | 1:220 | 6.5 mm |
| S | 1:64 | 22.4 mm (0.883″) |
| O | 1:48 (US); Europe mostly 1:45 or 1:43.5 | 32 mm (US 1.25″) |
| G | 1:22.5 | 45 mm |
Real-world sizes used in the examples (aircraft, vehicles, buildings) are typical published dimensions and are rounded; individual versions of a vehicle can differ.
Corrections
If you find an error, write to [email protected] with the page and the value. See also about this site.