What are Pythagorean triples?

Pythagorean triples are sets of three positive integers that satisfy a² + b² = c². Common triples: 3-4-5, 5-12-13, 8-15-17, 7-24-25. Any multiple of a triple is also a triple (e.g., 6-8-10 from 3-4-5).

Does this work for non-right triangles?

No. The Pythagorean theorem only applies to right triangles (triangles with one 90° angle). For other triangles, use the Law of Cosines: c² = a² + b² - 2ab×cos(C).

How do I know which side is the hypotenuse?

The hypotenuse is always the longest side and is directly opposite the right angle (90° angle). If you are given two sides and need to find the third, the hypotenuse must be longer than either of the other two sides.

Can I use this for 3D distance?

Yes, extend the theorem: d = √(x² + y² + z²). This calculates the straight-line distance between two points in 3D space. It is the 3D equivalent of the 2D distance formula.

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Pythagorean Theorem Calculator

Calculate the hypotenuse or a missing side of a right triangle using the Pythagorean theorem (a² + b² = c²). See the verification equation.

Last updated: March 31, 2026

Side a

Side b

How to Use This Calculator

Choose a mode: Find Hypotenuse or Find Missing Side.
For hypotenuse: enter the two shorter sides (a and b).
For missing side: enter the hypotenuse (c) and one known side.
Click Calculate to see all three sides with a verification equation.

The Formula

a² + b² = c², where c is the hypotenuse (longest side). Find c: c = √(a² + b²). Find a: a = √(c² - b²). The theorem only applies to right triangles (one 90° angle).

Frequently Asked Questions

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c². It was proven by the Greek mathematician Pythagoras around 500 BCE, though it was known to Babylonians much earlier.