Pythagorean Triples Calculator
This Pythagorean triples calculator can check if three given numbers form a Pythagorean triple and also generate Pythagorean triples via Euclid's formula!
Triples found16with hypotenuse up to 100
Smallest3, 4, 5
Showing16 of 16
TypePrimitive only
Pythagorean triples
| a | b | c | Area | Kind |
|---|---|---|---|---|
| 3 | 4 | 5 | 6 | primitive |
| 5 | 12 | 13 | 30 | primitive |
| 8 | 15 | 17 | 60 | primitive |
| 7 | 24 | 25 | 84 | primitive |
| 20 | 21 | 29 | 210 | primitive |
| 12 | 35 | 37 | 210 | primitive |
| 9 | 40 | 41 | 180 | primitive |
| 28 | 45 | 53 | 630 | primitive |
| 11 | 60 | 61 | 330 | primitive |
| 16 | 63 | 65 | 504 | primitive |
| 33 | 56 | 65 | 924 | primitive |
| 48 | 55 | 73 | 1,320 | primitive |
| 13 | 84 | 85 | 546 | primitive |
| 36 | 77 | 85 | 1,386 | primitive |
| 39 | 80 | 89 | 1,560 | primitive |
| 65 | 72 | 97 | 2,340 | primitive |
The formula
a = m² − n², b = 2mn, c = m² + n² (m > n > 0)
Euclid’s formula
Every primitive Pythagorean triple comes from two coprime integers m > n of opposite parity:
a = m² − n², b = 2mn, c = m² + n²
With m=2, n=1 that gives 3, 4, 5. Every other triple is a whole multiple of a primitive one — 6, 8, 10 is just 3, 4, 5 doubled.
What always holds
- The three angles add to 180°, without exception.
- Any two sides must add to more than the third — the triangle inequality. Sides of 4, 5 and 12 cannot close.
- The longest side always faces the largest angle.
Area = ½ × base × heightfor any triangle, with the height measured perpendicular to that base.
Which formula to reach for
With three sides, use Heron’s formula. With a base and its height, use ½bh. With two sides and the angle between them, use ½ab·sin C. With a right angle, the two legs are already base and height, so the area is just half their product.