Scale Calculator
Convert between real and scaled sizes for maps, models and drawings at any scale ratio.
20 m at common model scales
| Scale | Model size | In metres |
|---|---|---|
| HO (1:87) | 229.89 mm | 0.2299 m |
| OO (1:76) | 263.16 mm | 0.2632 m |
| N (1:160) | 125 mm | 0.125 m |
| O (1:48) | 416.67 mm | 0.4167 m |
| Car kit (1:24) | 833.33 mm | 0.8333 m |
| Figure (1:35) | 571.43 mm | 0.5714 m |
What a scale ratio means
A scale of 1:87 means one unit on the model equals 87 of the same unit in reality. The units cancel, so the ratio works with millimetres, inches or miles alike:
scale size = real size ÷ ratio
real size = scale size × ratio
A 20 m building at 1:87 becomes 230 mm.
Area and volume do not scale the same way
This is the part that catches people out. Halving every length quarters the area and cuts the volume to an eighth:
- Lengths scale by
1/n - Areas scale by
1/n² - Volumes — and therefore weights — scale by
1/n³
So an HO model at 1:87 has 1/7,569 of the surface area and about 1/658,503 of the mass of the real thing. It is also why paint coverage and material estimates cannot be scaled linearly.
Map scales
Maps use the same notation at much larger ratios. At 1:50,000, one centimetre on the paper is 500 m on the ground, and one inch is about 0.79 miles. A “large scale” map has a small ratio number and shows a small area in detail — the terminology is the reverse of what most people expect.
Model railway scales and gauges are different things. HO is 1:87 scale running on 16.5 mm gauge track; OO is 1:76 scale on the same gauge, which is why British models look slightly narrow-gauge.