The scale factor is the number you multiply a size by to get the scaled size: the new size divided by the original size.
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 40+ presets, or browse all scales.