Pythagorean Triples Calculator

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Pythagorean Triples Calculator

Generate primitive Pythagorean triples whose hypotenuse stays below a chosen limit.

Last updated: March 2026 | By ForgeCalc Engineering

Pythagorean Triples Solver

Triple generator

Calculation Info

1.Limit: 100
2.Use Euclid's formula: a = m^2 - k^2, b = 2mk, c = m^2 + k^2
3.Found 16 primitive triples within the limit.
Primitive Triples
(3, 4, 5)
(5, 12, 13)
(8, 15, 17)
(7, 24, 25)
(20, 21, 29)
(12, 35, 37)
(9, 40, 41)
(28, 45, 53)
(11, 60, 61)
(33, 56, 65)
(16, 63, 65)
(48, 55, 73)
(13, 84, 85)
(36, 77, 85)
(39, 80, 89)
(65, 72, 97)

What Pythagorean Triples Mean

A Pythagorean triple is a set of three positive integers that satisfy a^2 + b^2 = c^2. Primitive triples share no common factors greater than 1.

How to Generate Pythagorean Triples

  1. Choose a limit for the hypotenuse.
  2. Generate Euclid parameters m and k.
  3. Filter to primitive triples with odd/even parity rules.
  4. Collect triples whose hypotenuse stays below the limit.
a = m^2 - k^2, b = 2mk, c = m^2 + k^2

Worked Example

Example: (3, 4, 5) is a primitive Pythagorean triple.

3^2 + 4^2 = 5^2

Frequently Asked Questions

What makes a triple primitive?

The three numbers share no common factor greater than 1.

Does the limit apply to all sides?

The limit is applied to the hypotenuse c.

Can I get non-primitive triples?

This version generates primitive triples only.

Does this accept decimals?

No. The generator works with integer parameters and limits.

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