Scale factor calculator
Doubling a length quadruples the area and multiplies the volume by eight. That square-cube relation is what this makes explicit.
For a 1:87 model, enter 87.
Model dimension
51.724 137 93
- Real dimension from a model one
- 391 500
- Area divides by
- 7569
- Volume divides by
- 658 503
- Scale as a percentage
- 1.149 43 %
Show the working
- Real dimension = 4500
- Scale denominator = 87
- Model dimension = 4500 / 87 = 51.7241
- Area divides by = 87^2 = 7569
- Volume divides by = 87^3 = 658 503
- Real dimension from a model one = 4500 * 87 = 391 500
- Scale as a percentage = 100 / 87 = 1.149 43
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- model = real / scale
- areas scale as the square, volumes as the cube
A 1:87 HO model is 1.149% of full size in length, 0.0132% in area and 0.000152% in volume.