Pythagorean Theorem Calculator

a² + b² = c² — find the hypotenuse or a missing leg.

Hypotenuse (c)
5

a² + b² = c² — the foundational relationship between the sides of any right triangle, named for the ancient Greek mathematician Pythagoras.

A worked example

Legs of 3 and 4 give a hypotenuse of exactly 5. And a hypotenuse of 13 with one leg of 5 gives the other leg as exactly 12.

Frequently asked questions

What's a Pythagorean triple?

A set of three whole numbers that satisfy a² + b² = c² exactly — like 3-4-5 or 5-12-13. They're useful as quick mental reference points and show up often in textbook problems.

Does this work for any triangle, or just right triangles?

Only right triangles — the Pythagorean theorem specifically relies on the 90° angle. For any other triangle, use the Triangle Calculator, which applies the more general Law of Cosines instead.