How this calculator works
A Pythagorean triple consists of positive integers satisfying the right triangle equation. Checking uses exact integer arithmetic, so a large square is not rounded. Generation uses Euclid parameters and permits any positive scale k. The generated legs may appear in either order. A primitive triple has no common integer factor greater than one.
Formula
Check: a²+b²=c² with c the largest. Generate: a=k(m²-n²), b=2kmn, c=k(m²+n²), where m>n>0.
Worked example
m = 2, n = 1 and k = 1 give 3, 4 and 5. With m = 3 and n = 2 the triple is 5, 12 and 13. Scaling the first triple by 2 gives 6, 8 and 10, which is not primitive.
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Frequently asked questions
Must m and n be coprime?
No, but primitive output requires coprime m and n of opposite parity and k = 1. Other choices still give valid triples.
Why are decimals rejected?
A Pythagorean triple is an integer concept. Use the right triangle calculator for arbitrary positive side lengths.
What is the input limit?
Each input is limited to a positive safe JavaScript integer. Generated integers are calculated and displayed exactly as text, even if larger than that limit.