About the Pythagorean Triples Generator
A Pythagorean triple is a set of three whole numbers that fit the Pythagorean theorem, a² + b² = c², like 3, 4, 5. They are the sides of right triangles with whole-number lengths. This generator lists all the triples whose longest side is no bigger than the limit you choose. You can show only the primitive ones, which share no common factor, or all, and search for triples that contain a given number. Type the largest hypotenuse, whether to show only primitive triples, and optionally a number to look for and the Pythagorean triples appears at once, with a few related figures underneath, and you can copy the result with one tap. The sums run in your browser, so nothing you enter is uploaded.
Updated October 2026
How to use the Pythagorean Triples Generator
- 1Enter the largest hypotenuse, whether to show only primitive triples, and optionally a number to look for.
- 2Pick the units or options from the menus if the Pythagorean triples tool offers them.
- 3Read the Pythagorean triples in the large result box.
- 4Look at the extra rows for related figures.
- 5Press Copy result to keep the answer.
When you need the Pythagorean triples
Carpenters use 3-4-5 to make a square corner, because a triangle with those sides must be right-angled. Teachers use triples for problems that come out in whole numbers, and number-theory fans enjoy their patterns.
Every multiple of a triple is also a triple, so 3-4-5 leads to 6-8-10, 9-12-15 and so on. The primitive ones are the building blocks. The tool lists each triple with the shorter leg first.
How the Pythagorean triples is worked out
Euclid's formula: for whole numbers m > n, a = m² − n², b = 2mn, c = m² + n² gives a triple. It is primitive when m and n share no factor and are not both odd. Up to a hypotenuse of 50 there are seven primitive triples: 3-4-5, 5-12-13, 8-15-17, 7-24-25, 20-21-29, 12-35-37 and 9-40-41. Including multiples, up to 100 there are 52 triples in all, such as 6-8-10 and 9-12-15.
Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.
- Primitive or all
- Search by a number
- Up to hypotenuse 5,000
Mistakes to avoid with Pythagorean triples
The search for a number finds triples where it appears as any of the three sides. The limit is 5,000 for the hypotenuse, and at most 300 lines are shown. A number can appear in many triples or in none, as 2 does.
On phone and computer
On a phone, type into the boxes one after another and read the Pythagorean triples underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the Pythagorean triples move. The pythagorean triples generator works the same on both. Triples are whole-number right triangles, and other tools use them for checks. Use the Pythagorean Theorem Calculator for any sides, the Triangle Calculator for angles, and the Factor Calculator to see why a triple works.
Features
- Multiples of triples are triples
- 3-4-5 squares a corner
- Limit of 300 lines shown
- Clear messages when the Pythagorean triples inputs make no sense
- Copy the result with one tap
- Private: nothing is uploaded
Frequently asked questions
How do I calculate Pythagorean triples?
Euclid's formula: for whole numbers m > n, a = m² − n², b = 2mn, c = m² + n² gives a triple. It is primitive when m and n share no factor and are not both odd. Up to a hypotenuse of 50 there are seven primitive triples: 3-4-5, 5-12-13, 8-15-17, 7-24-25, 20-21-29, 12-35-37 and 9-40-41. Including multiples, up to 100 there are 52 triples in all, such as 6-8-10 and 9-12-15.
What is the formula for Pythagorean triples?
Euclid's formula: for whole numbers m > n, a = m² − n², b = 2mn, c = m² + n² gives a triple. It is primitive when m and n share no factor and are not both odd. The pythagorean triples generator applies it exactly and rounds only the displayed answer to six significant figures.
How do carpenters use 3-4-5?
They mark 3 units on one board, 4 on the other and check the diagonal is 5. If it is, the corner is square.
Are there infinitely many triples?
Yes. Euclid's formula gives one for every pair m > n.
Is there a triple with 2?
No, 2 cannot be a side of an integer right triangle.
Is this pythagorean triples generator free and private?
Yes. It is free, needs no account and runs in your browser, so the numbers you type are not uploaded or stored.