How this calculator works
A scale factor is the ratio of a drawn size to the real size. Length scales in one dimension, but area scales with the square of the factor and volume with its cube. A 1 : 50 drawing therefore reduces lengths by 50, areas by 2,500 and volumes by 125,000. When you solve for the factor from two areas or volumes, the calculator takes the square root or cube root so the answer is still a length scale that you can compare with a drawing ratio.
Formula
length factor = scaled length / real length. scaled length = real length x factor. real length = scaled length / factor. scaled area = real area x factor^2. scaled volume = real volume x factor^3. To recover a length factor from areas use the square root of scaled / real; from volumes use the cube root.
Worked example
At 1 : 50, a real 5 m wall is 0.1 m or 10 cm on the drawing. A real 1 m2 floor becomes 0.0004 m2 on the drawing, and a real 1 m3 tank becomes 0.000008 m3. Entering a 400 cm2 drawing area and a 1 m2 real area gives a length factor of 0.02, or 1 : 50.
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Frequently asked questions
Why is the area factor squared?
Both the width and the height are scaled, so the area ratio is the length ratio multiplied by itself. A 1 : 50 drawing shrinks area by 50 x 50 = 2,500.
Why is the volume factor cubed?
Length, width and height each carry the factor, so volume scales by the cube. A 1 : 50 model has 1/125,000 of the real volume.
Which way round is a 1 : 50 scale?
The first number is the drawing and the second is the real object. One unit on the drawing represents 50 of the same units in real life, so the length factor is 1/50 = 0.02.