Pythagorean Triples Calculator

Pythagorean Triples Calculator

Find triples, verify a triple, or generate one from Euclid's formula.

Last updated: June 2026 | By Patchworkr Team

Result
Click Calculate to see the output for the selected mode.

Formulas

Find Triples
a = m^2 - n^2, b = 2mn, c = m^2 + n^2
Verify
a^2 + b^2 = c^2
Generate
m > n ≥ 1, gcd(m,n)=1

How to Use

Choose a mode, enter the required values, and click calculate. The generator and finder follow Euclid's formula, while verify checks the Pythagorean equation directly.

  1. Select a mode.
  2. Enter the required values for that mode.
  3. Read the result card.

Example

Verify 5, 12, 13 to confirm a primitive Pythagorean triple.

Use m = 4 and n = 1 to generate the same triple from Euclid's formula.

Notes

The old behavior is preserved, but the inputs are now parsed more explicitly and the layout matches the newer card pattern.

Only integer m and n values are accepted for generation, and the generator requires m > n ≥ 1.

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