education
Scale Factor Calculator
Last updated: May 31, 2026
Written by Blake Boege
A scale factor calculator is a geometry utility that calculates the scaling ratio between two similar figures or scales a given dimension up or down. It calculates the multiplier by dividing the scaled size by the original size, showing the percentage changes and whether it represents an enlargement or reduction. It is commonly used in blueprints, mapping, design modeling, and similarity problems.
Find the scale factor between two dimensions, or enter an original length and scale factor to compute the new dimension.
Quick Answer
Find scale factors between two similar shapes or scale any geometry dimension up or down. Renders scale calculations and ratios.
Calculation Mode
The linear size of the original figure. · e.g. 10
The linear size of the scaled/similar figure. · e.g. 25
Calculated Scale Factor (k)
2.5
Scale factor affects area by the square of the factor (k²) and volume by the cube of the factor (k³).
Examples
Original = 5m, Scaled = 15m
Scale Factor = 15 ÷ 5 = 3 (Enlargement)
Original = 10m, Scaled = 2m
Scale Factor = 2 ÷ 10 = 0.2 (or 1:5 Reduction)
How it works
Choose between finding the scale factor of two shapes or scaling an original size by a factor.
Formula (Find Factor) · k = Scaled / Original
Formula (Scale Size) · Scaled = Original × k
Understanding scale factor
Scale factors are widely used in blueprinting, model building, maps, and geometry. The scale factor is a multiplier:
When solving ratios on maps (e.g., 1:100), the scale factor is 1/100 = 0.01, meaning every unit on the map is 100 times larger in real life.
Related math calculators
For ratios and proportions, check out these related math tools:
- Ratio Calculator — simplify ratios and find equivalent ratios.
- Proportion Calculator — solve proportion equations (like a/b = c/d).
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Frequently asked questions
A scale factor is a number by which all the dimensions of a geometric figure are multiplied to create a similar figure that is either larger or smaller. It is the ratio of a new dimension to its corresponding original dimension.
The formula is: Scale Factor = Scaled Dimension ÷ Original Dimension. For example, if a 4-inch side is scaled up to 12 inches, the scale factor is 12 ÷ 4 = 3.
If the scale factor is greater than 1, the new figure is larger (scaling up or enlargement). If the scale factor is between 0 and 1, the new figure is smaller (scaling down or reduction).
Multiply the original length by the scale factor to find the new scaled length: Scaled Length = Original Length × Scale Factor.
If a shape's linear dimensions are multiplied by a scale factor k, its area is multiplied by k² and its volume is multiplied by k³.
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