Pythagorean Theorem Calculator

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c, the longest side opposite the right angle) equals the sum of the squares of the other two sides: a² + b² = c². It was known to Babylonian mathematicians over 3,000 years ago but is named after the Greek mathematician Pythagoras (570-495 BC), who is credited with the first formal proof.

A Pythagorean triple is a set of three positive integers (a, b, c) that satisfy a² + b² = c². The most famous is 3, 4, 5 (9+16=25). Multiples of any triple also form triples: 6, 8, 10 or 9, 12, 15. Pythagorean triples are used in construction to verify right angles — a 3-4-5 triangle is the simplest way to create a perfect 90° corner on a building site.

To find the hypotenuse (c) when you know both legs: c = √(a² + b²). For example, with legs 3 and 4: c = √(9+16) = √25 = 5. To find a leg when you know the hypotenuse and other leg: a = √(c² - b²). With c=5, b=4: a = √(25-16) = √9 = 3. Enter any two known sides in our calculator above for instant results.