Triangle Scale Factor Calculator — Similar Triangles & Scaling
Enter the sides of both triangles to find the scale factor k and verify similarity, or enter one triangle and a scale factor to generate the enlarged or reduced triangle instantly.
Mode
Triangles are similar — every side ratio equals k
- 1
Ratio a₂ / a₁
6 ÷ 3 = 2 - 2
Ratio b₂ / b₁
8 ÷ 4 = 2 - 3
Ratio c₂ / c₁
10 ÷ 5 = 2 - 4
Scale factor k (average)
(2 + 2 + 2) ÷ 3 = 2Average of the three side ratios; equals the exact k when triangles are similar.
How does this calculator work?
The scale factor k between two similar triangles equals the ratio of any pair of corresponding sides: k = a₂/a₁. Perimeters scale by k, areas by k². Enter both triangles' sides to verify similarity and compute k, or enter one triangle and k to generate the scaled copy.
Formula
How this is calculated
When two triangles are similar, every pair of corresponding sides shares the same ratio, called the scale factor k. To find it, divide each side of Triangle 2 by the matching side of Triangle 1: k = a₂/a₁ = b₂/b₁ = c₂/c₁. If the three ratios agree (within rounding tolerance), the triangles are similar and k is exact; if they differ, the triangles are not similar and the calculator flags this, showing the average ratio as an approximation.
Linear measurements — side lengths and perimeter — scale by k, so Perimeter₂ = k × Perimeter₁. Areas scale by the square of k, since area is a two-dimensional quantity: Area₂ = k² × Area₁. A triangle scaled by k = 2 has 4× the area; scaled by k = 0.5 it has ¼ the area.
In "scale by factor k" mode the calculator multiplies every side of Triangle 1 by k to produce Triangle 2, which is guaranteed similar. This is useful when you want to design a scaled copy — for example, resizing a triangular architectural element or computing the dimensions of a model at a given scale ratio.
Frequently asked questions
Yes — enter corresponding sides in the same position (the side labelled a₁ in Triangle 1 must correspond to a₂ in Triangle 2). Typically pair shortest with shortest, longest with longest. If the ratios come out inconsistent, re-order the Triangle 2 sides until they match.
Perimeter is a sum of lengths, each multiplied by k, so the total is k times longer. Area is computed from base × height (or equivalently from Heron's formula), and both base and height are lengths that scale by k — their product scales by k × k = k².
Yes — the "both triangles' sides" mode accepts any two valid triangles. If the three side ratios differ the calculator shows the average k and an informational message. This can help you see by how much the triangles deviate from similarity.
Also known as
TG we-Calculate Editorial Team. (2026). Triangle Scale Factor Calculator — Similar Triangles & Scaling [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/triangle-scale-factor-calculator
TG we-Calculate Editorial Team. "Triangle Scale Factor Calculator — Similar Triangles & Scaling." TG we-Calculate. 2026. https://we-calculate.com/calculator/triangle-scale-factor-calculator.
TG we-Calculate Editorial Team, "Triangle Scale Factor Calculator — Similar Triangles & Scaling," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/triangle-scale-factor-calculator
@misc{wecalculate_triangle_scale_factor_calculator, title = {Triangle Scale Factor Calculator — Similar Triangles & Scaling}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/triangle-scale-factor-calculator}}, year = {2026}, note = {TG we-Calculate} }
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