Scale Factor Calculator
The scale factor is the ratio between corresponding measurements of two similar figures. Enter a measurement from the original figure and the corresponding measurement from the scaled figure, and this calculator finds the scale factor k. It also calculates how area and volume scale: area scales by k² and volume scales by k³. For example, a scale factor of 2 means all linear measurements double, area quadruples, and volume octuples. This calculator is essential for understanding similar shapes, map scales, architectural models, and image resizing.
Scale factor formulas
Scale factor: k = scaled measurement / original measurement
Scaled linear measurement = original * k
Area scale factor = k²
Volume scale factor = k³
Worked example
Original side length: 5 units. Scaled side length: 10 units.
- Scale factor k = 10 / 5 = 2
- Area scales by k² = 2² = 4 (area becomes 4 times larger)
- Volume scales by k³ = 2³ = 8 (volume becomes 8 times larger)
Scale factor calculator: frequently asked questions
What is a scale factor?
A scale factor is the ratio between corresponding linear measurements of two similar figures. If a scale factor is k, then a linear measurement in the scaled figure is k times the original. For example, if the scale factor is 2, all sides are twice as long. If the scale factor is 0.5, all sides are half as long.
How do I find the scale factor?
Divide the measurement of the scaled figure by the corresponding measurement of the original figure. For example, if the original side is 5 units and the scaled side is 10 units, the scale factor is 10 / 5 = 2. Conversely, if the scaled side is 2.5 units, the scale factor is 2.5 / 5 = 0.5.
How does scale factor affect area and volume?
If the scale factor is k, then the area of the scaled figure is k² times the original area. The volume of the scaled figure is k³ times the original volume. For example, with a scale factor of 2, the area increases by a factor of 4, and the volume increases by a factor of 8.
What are similar figures?
Similar figures have the same shape but different sizes. All corresponding angles are equal, and all corresponding sides are proportional. Triangles are similar if all corresponding angles match (AA similarity). Polygons are similar if all corresponding sides have the same ratio.
Where is scale factor used?
Scale factors are used in map making (map scale), architecture (scale models), engineering drawings, photography (magnification), and video/image resizing. In education, scale factors help understand proportional relationships and similarity.
Official sources
- Geometry and similarity: National Institute of Standards and Technology.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.