Solve Similar Triangles Calculator
Two triangles are similar when their angles match and their sides are proportional. Enter the three sides of the first triangle and any one corresponding side of the second triangle to instantly find the scale factor k and all remaining sides.
Corresponds to side
Each side of Triangle 2 = k × corresponding side of Triangle 1
- 1
Triangle 1 side (a)
3 - 2
Known side (Triangle 2)
6 - 3
Scale factor k
6 ÷ 3 = 2Every side of Triangle 2 equals k times the corresponding side of Triangle 1.
How does this calculator work?
Similar triangles have the same angles; their sides are proportional with scale factor k = side₂ / side₁. Enter all three sides of the first triangle and one known side of the second to get k and all remaining sides. Areas scale by k² while perimeters scale by k.
Formula
How this is calculated
When two triangles are similar (AA, SAS, or SSS similarity), their corresponding sides share a fixed ratio called the scale factor k. If Triangle 1 has sides a, b, c and Triangle 2 has corresponding sides a′, b′, c′, then a′/a = b′/b = c′/c = k. Knowing k and any three sides of one triangle gives all sides of the other.
This calculator derives k from the one known corresponding pair you supply, then multiplies each side of Triangle 1 by k to get all three sides of Triangle 2. The perimeters scale by the same factor k, while areas scale by k² — so a triangle with k = 2 has 4× the area of the original.
The Heron formula is used to compute areas from the three side lengths; it works for any valid triangle. Note that this calculator does not verify whether the given sides actually form a valid triangle — if the three sides violate the triangle inequality (any side must be less than the sum of the other two) the area will be zero or imaginary. Angles can be computed from the sides with the law of cosines if needed.
Frequently asked questions
Two triangles are similar if all three pairs of corresponding angles are equal (AA criterion), or equivalently, all three pairs of corresponding sides are proportional (SSS similarity). The triangles have the same shape but can differ in size.
Area scales by k² (the square of the linear scale factor). If k = 3 the similar triangle has 9× the area of the original. Perimeter, by contrast, scales linearly by k.
Yes — two right triangles sharing one acute angle are always similar (AA). Enter the two legs and hypotenuse, supply the corresponding known side of the second triangle, and the calculator gives the remaining two sides.
Also known as
TG we-Calculate Editorial Team. (2026). Solve Similar Triangles Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/solve-similar-triangles-calculator
TG we-Calculate Editorial Team. "Solve Similar Triangles Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/solve-similar-triangles-calculator.
TG we-Calculate Editorial Team, "Solve Similar Triangles Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/solve-similar-triangles-calculator
@misc{wecalculate_solve_similar_triangles_calculator, title = {Solve Similar Triangles Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/solve-similar-triangles-calculator}}, year = {2026}, note = {TG we-Calculate} }
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