What is the triangle scale factor?
When two triangles are similar, they have the same shape but different sizes. The scale factor (\(k\)) is the constant ratio between every pair of corresponding sides. If you know one matching pair of sides, you know the scale factor for the entire figure — and you can find any missing side.
How to use this calculator
Enter a side of the first triangle and its corresponding side on the second triangle. The calculator divides the second by the first to get \(k\). Optionally enter another side from Triangle 1 to instantly see its scaled length on Triangle 2. The tool also reports the area scale factor, which is \(k^{2}\).
The formula explained
The core relationship is $$k = \frac{\text{Side (Triangle 2)}}{\text{Side (Triangle 1)}}$$ A factor greater than 1 means an enlargement; between 0 and 1 means a reduction. Because area grows with the square of length, areas of similar triangles relate by \(k^{2}\), while perimeters relate by \(k\) itself.
Worked example
Suppose a triangle has a 4 cm side that corresponds to a 6 cm side on a larger similar triangle. Then $$k = 6 \div 4 = \textbf{1.5}$$ Another side measuring 5 cm on the small triangle becomes $$5 \times 1.5 = \textbf{7.5 cm}$$ and the larger triangle's area is \(1.5^{2} = \mathbf{2.25}\) times bigger.
FAQ
Which side do I divide by which? Put the original (reference) triangle's side as side₁ and the target triangle's matching side as side₂. \(k > 1\) enlarges, \(k < 1\) shrinks.
Does the scale factor apply to angles? No. Similar triangles keep identical angles regardless of size; only lengths scale.
How do areas scale? Multiply the original area by \(k^{2}\). If sides triple (\(k = 3\)), area becomes 9 times larger.
