What this calculator does
Pythagorean triple generator works out builds a right-triangle integer triple from two generator numbers (Euclid’s formula). Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
Formulaa = m²−n², b = 2mn, c = m²+n² for m > n > 0; primitive when gcd(m,n)=1 and m, n have opposite parity
The inputs explained
| Field | What to enter |
|---|---|
| m (larger generator) | A number. Starts at 2. |
| n (smaller generator) | A number. Starts at 1. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with m (larger generator)
Every other input is held at the calculator’s starting values while m (larger generator) varies. Select any row to load that scenario into the calculator.