Scale Factor Calculator
Enter original and scaled measurements to compute the scale factor, scaled dimensions, and see how area and volume change with scaling.
Result
Scaling Effects
Step-by-Step
What Is a Scale Factor?
A scale factor describes how much a figure has been enlarged or reduced relative to its original. In similar figures, all corresponding lengths share the same ratio — this ratio is the scale factor. It's ubiquitous in architecture (blueprints), cartography (maps), model-making, and even digital design (responsive scaling).
While lengths scale linearly by k, area scales by k² and volume scales by k³. This means doubling all dimensions of a box makes it 4 times the surface area and 8 times the volume — a critical insight for engineers, architects, and scientists working with scaled models.
Scaling Powers
Length
Scales by k
Area
Scales by k²
Volume
Scales by k³
How to Use the Scale Factor Calculator
Find or apply scale factors in three steps.
Choose Mode
Select "Find Scale Factor" if you have two measurements, or "Scale a Measurement" if you have the factor.
Enter Values
Type the original length and the new length (or the scale factor k).
View Results
See the scale factor, how area and volume scale, whether it's an enlargement or reduction, and more.
Worked Examples
Four scale factor problems with solutions.
1Original = 5 cm, Scaled = 15 cm+−
2Model 1:50 — original 200 m+−
3Photo 4×6 scaled to 8×12+−
4Original 12 in, scale factor 0.5+−
Frequently Asked Questions
Common questions about scale factors.
What is a scale factor?+−
A scale factor is the ratio of corresponding lengths between two similar figures. If the scale factor from A to B is 2, every length in B is twice the corresponding length in A.
How do I calculate the scale factor?+−
Divide any measurement on the new (scaled) figure by the corresponding measurement on the original figure: Scale Factor = New ÷ Original.
What does a scale factor less than 1 mean?+−
A scale factor between 0 and 1 means the scaled figure is a reduction (smaller). A scale factor greater than 1 is an enlargement.
How does scale factor affect area and volume?+−
Area scales by the square of the scale factor (k²), and volume scales by the cube (k³). So a scale factor of 3 means 9× the area and 27× the volume.
What is the scale factor in maps?+−
Map scale (e.g., 1:50,000) means 1 unit on the map equals 50,000 units in reality. The scale factor is 1/50,000.
Can scale factors be negative?+−
In basic geometry, scale factors are positive. However, in transformations, a negative scale factor indicates a reflection combined with scaling.
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