Scale Factor Calculator
Find a scale factor between two lengths, or apply one to a length, below.
Finding a Scale Factor
Scale factor = scaled length ÷ original length.
Scale factor shows up constantly in maps, blueprints, and models. A map scale of 1:24,000 means 1 unit on the map equals 24,000 of the same unit in real life — so 1 inch on that map represents 24,000 inches, or 2,000 feet, on the ground.
Worked example
A model is scaled from 4 inches to 10 inches.
10 ÷ 4 = 2.5
Scale factor: 2.5×
A second example, shrinking instead of enlarging: a photo is scaled from 8 inches wide down to 5 inches wide.
5 ÷ 8 = 0.625
Scale factor: 0.625×
Common mistake
It's easy to apply a scale factor to area or volume the same way you would to length. If a shape's sides double (scale factor 2), its area doesn't double — it quadruples (2² = 4), and its volume increases eightfold (2³ = 8).
Keep going
- The golden ratio is one specific, famous scale factor, about 1.618; the golden ratio calculator applies that exact fixed ratio instead of one you choose. Golden Ratio Calculator
Frequently Asked Questions
How do you find a scale factor?
Divide the new (scaled) length by the original length: scale factor = scaled ÷ original.
What does a scale factor greater than 1 mean?
It means the shape or object was enlarged. A scale factor between 0 and 1 means it was shrunk, and a scale factor of exactly 1 means the size didn't change.
Does scale factor apply to area and volume the same way as length?
No. If lengths scale by a factor k, area scales by k², and volume scales by k³ — this is why a small increase in a model's scale can mean a much larger increase in its volume.
How do you apply a scale factor to a length?
Multiply the original length by the scale factor. A 6-inch side with a scale factor of 1.5 becomes 6 × 1.5 = 9 inches.
What does a map scale like 1:24,000 mean?
It's a scale factor written as a ratio: 1 unit on the map equals 24,000 of the same unit in real life. So 1 inch on that map represents 24,000 inches, or 2,000 feet, on the ground.
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