Similar Triangles Calculator — Scale Factor & Missing Sides
Two triangles are similar if their corresponding angles are equal and their sides are proportional. Enter all three sides of the reference triangle and one corresponding side of the second triangle — the calculator finds the scale factor and the remaining two sides.
Triangle 2 sides = k × Triangle 1 sides
- 1
Corresponding side in △₁ (a₁)
6 - 2
Corresponding side in △₂ (a₂)
9 - 3
Scale factor k = a₂ ÷ a₁
9 ÷ 6 = 1.5000All Triangle 2 sides = k × the corresponding Triangle 1 side.
How does this calculator work?
For two similar triangles, divide any known corresponding side of Triangle 2 by its counterpart in Triangle 1 to get scale factor k. All Triangle 2 sides = k × Triangle 1 sides; the area scales by k². Enter three sides of the reference triangle and one corresponding side of the second to solve for the rest.
Formula
How this is calculated
Two triangles are similar (written △₁ ~ △₂) when their corresponding angles are equal — this guarantees that corresponding sides are in a constant ratio, called the scale factor k. Knowing any pair of corresponding sides immediately gives k = a₂ / a₁, and every other side of the second triangle follows: b₂ = k × b₁ and c₂ = k × c₁.
Perimeters also scale by k (perimeter₂ = k × perimeter₁), while areas scale by k² — doubling all sides quadruples the area. This quadratic scaling is why this calculator reports both the linear scale factor and the area ratio separately.
The calculator validates that the three sides of Triangle 1 satisfy the triangle inequality (the sum of any two sides must exceed the third). If they do not, no real triangle exists and no result is returned. The actual shape of the triangle — whether it is acute, right or obtuse — does not affect the similarity calculation, only the scale factor matters.
Frequently asked questions
Yes — similarity ratios only hold between corresponding sides (shortest to shortest, longest to longest, etc.). If you enter side a₁ as the base and a₂ as the corresponding base of the similar triangle, the calculator correctly derives b₂ and c₂. Mismatching sides gives an incorrect scale factor.
Yes — the scale factor is the same regardless of which pair you use. If you know b₁ and b₂ instead, just relabel them as a₁ and a₂ in the input fields. The ratio a₂/a₁ will equal b₂/b₁ = c₂/c₁ for truly similar triangles.
Congruent triangles are a special case of similar triangles where k = 1 — the triangles have identical dimensions, not just the same shape. Similar triangles have the same angles but different sizes (k ≠ 1).
Also known as
TG we-Calculate Editorial Team. (2026). Similar Triangles Calculator — Scale Factor & Missing Sides [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/similar-triangles-calculator
TG we-Calculate Editorial Team. "Similar Triangles Calculator — Scale Factor & Missing Sides." TG we-Calculate. 2026. https://we-calculate.com/calculator/similar-triangles-calculator.
TG we-Calculate Editorial Team, "Similar Triangles Calculator — Scale Factor & Missing Sides," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/similar-triangles-calculator
@misc{wecalculate_similar_triangles_calculator, title = {Similar Triangles Calculator — Scale Factor & Missing Sides}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/similar-triangles-calculator}}, year = {2026}, note = {TG we-Calculate} }
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