Triangle Similarity Calculator — SSS & AA Criteria
Enter the sides (SSS) or two angles (AA) of both triangles to instantly determine whether they are similar, compute the scale factor, and find the area and perimeter ratios.
Similarity criterion
Ratio of corresponding sides (Triangle 2 / Triangle 1)
- 1
Ratio of smallest sides
6 ÷ 3 = 2 - 2
Ratio of middle sides
8 ÷ 4 = 2 - 3
Ratio of largest sides
10 ÷ 5 = 2 - 4
Scale factor k (average)
(2 + 2 + 2) ÷ 3 = 2All three ratios are equal (within tolerance) when the triangles are similar.
How does this calculator work?
SSS: sort both triangles' sides and check a₂/a₁ = b₂/b₁ = c₂/c₁ = k. AA: if two angle pairs match, all three do and the triangles are similar. Enter side pairs or angle pairs — the calculator confirms similarity, reports k, and gives the area ratio k² and perimeter ratio k.
Formula
How this is calculated
Two triangles are similar (△₁ ~ △₂) when they have the same shape but not necessarily the same size. There are two equivalent ways to verify this.
SSS similarity (three pairs of sides): Sort both triangles' sides from smallest to largest, then check whether the three ratios — smallest/smallest, middle/middle, largest/largest — are all equal. If they are, the common ratio is the scale factor k. The calculator allows up to 0.5% relative tolerance to absorb rounding in real-world measurements. Once k is confirmed, the area ratio is k² and the perimeter ratio is k.
AA similarity (two angle pairs): If two angles of one triangle equal two corresponding angles of the other, the triangles are automatically similar — because the third angles must also be equal (they each sum to 180°). The calculator sorts both angle sets and compares them within 0.01° tolerance. AA similarity says nothing about the scale factor since no side lengths are involved.
Note that SSS similarity differs from SSS congruence: congruence requires equal sides, while similarity only requires proportional sides.
Frequently asked questions
SSS congruence requires all corresponding sides to be equal (k = 1). SSS similarity only requires that the ratios of corresponding sides are equal — any constant k qualifies. Congruent triangles are a special case of similar triangles.
No — the calculator sorts both triangles' sides internally before comparing ratios. Just make sure to enter corresponding sides in matching positions (shortest to shortest, longest to longest) to interpret the individual ratios correctly.
Yes — but only if k = 1 (they are congruent). If k ≠ 1, the areas differ by k². So two non-congruent similar triangles always have different areas.
Also known as
TG we-Calculate Editorial Team. (2026). Triangle Similarity Calculator — SSS & AA Criteria [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/triangle-similarity-calculator
TG we-Calculate Editorial Team. "Triangle Similarity Calculator — SSS & AA Criteria." TG we-Calculate. 2026. https://we-calculate.com/calculator/triangle-similarity-calculator.
TG we-Calculate Editorial Team, "Triangle Similarity Calculator — SSS & AA Criteria," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/triangle-similarity-calculator
@misc{wecalculate_triangle_similarity_calculator, title = {Triangle Similarity Calculator — SSS & AA Criteria}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/triangle-similarity-calculator}}, year = {2026}, note = {TG we-Calculate} }
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