Carpenters have squared foundations for centuries with a 3-4-5 rope: stake 3 feet one way, 4 feet the other, and a 5-foot diagonal guarantees a perfect right angle. That works because 3² + 4² = 5² — a Pythagorean triple, three whole numbers satisfying a² + b² = c². Euclid's formula manufactures infinitely many: pick any m > n, and (m² − n², 2mn, m² + n²) is a triple. With m = 2, n = 1 you get (3, 4, 5); with m = 3, n = 2 you get (5, 12, 13); with m = 4, n = 1 you get (15, 8, 17).

Multiples count too — (6, 8, 10) is just (3, 4, 5) doubled — but the primitive triples from Euclid's formula are the interesting ones, and they always come with one even leg, one odd leg, and an odd hypotenuse. Surveyors, navigators, and game developers use triples to get exact right angles and clean distances without square roots. This calculator verifies the defining equation: type a² + b²'s value in the Variable A box — for (5, 12, 13), that is 25 + 144 = 169 — and type 1 in the Variable B box. The Result box shows 169; since 13² = 169 matches, the triple checks out. Mismatched results mean the numbers are not a triple.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Pythagorean Triples Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.