What is a scale factor?
The scale factor is the number you multiply a real measurement by to get the scaled (model or drawing) measurement. It is simply the new size divided by the original size, using the same unit for both:
scale factor = scaled size ÷ original size
A scale factor below 1 is a reduction (a model smaller than the real object); above 1 is an enlargement. A factor of 0.0417 is the same as the ratio 1:24, because 1 ÷ 0.0417 = 24.
Area and volume scale differently
When you scale a shape, its area changes by the factor squared and its volume by the factor cubed. So a 1:10 model is 10× shorter, but has only 1/100 of the surface area and 1/1000 of the volume — which is why paint and material needs drop so fast at small scales. The calculator shows the area (ײ) and volume (׳) factors for you.
Worked example
A real car is 4.8 m long and you want a 20 cm model. Convert to the same unit (0.2 m), then divide: 0.2 ÷ 4.8 = 0.0417, or 1:24. Its model area is ×0.0017 and volume ×0.00007 of the real car.
Frequently asked questions
What is a scale factor?
A scale factor is the number you multiply a size by to get the scaled size. It equals the new size divided by the original size — for example, a 20 cm model of a 4.8 m car has a scale factor of 0.0417, or 1:24.
How do I calculate the scale factor between two sizes?
Divide the new (scaled) size by the original size, using the same unit for both. 0.2 m ÷ 4.8 m = 0.0417, which is the same as 1:24.
How does the scale factor affect area and volume?
Area scales by the factor squared and volume by the factor cubed. At a scale factor of 1/2, area is 1/4 and volume is 1/8 — so a model at 1:10 has 1/100 of the area and 1/1000 of the volume.
How do I scale a measurement up or down by a percentage?
Multiply the size by the percentage ÷ 100. To enlarge by 150%, multiply by 1.5; to reduce to 40%, multiply by 0.4.
Looking for a specific scale? Try the scale calculator with 50+ presets, or browse all scales.