Pythagorean theorem calculator

Type the two legs, such as 3, 4, and the calculator finds the hypotenuse. To find a leg instead, set "Two numbers are" to a leg and c, then type the leg you know and the hypotenuse.

You can also label the sides, as in a = 8, c = 17, and it solves for whichever one is missing. Type three sides to check whether they make a right triangle.

Whole-number sides give an exact answer as well as a decimal. With legs of 5 and 5 the hypotenuse is √50, which simplifies to 5√2, about 7.07.

In a right triangle, the square on the longest side equals the two other squares added together: a² + b² = c². The longest side, c, is the hypotenuse, and it always sits opposite the right angle.

To find c, square the legs, add them and take the square root. For a leg, square the hypotenuse, subtract the square of the leg you know and take the square root of what's left.

Some right triangles have whole-number sides, like 3, 4, 5 and 5, 12, 13. These sets are called Pythagorean triples. Any multiple of one is another, so 6, 8, 10 works too.

A Babylonian clay tablet known as Plimpton 322, written around 1800 BC, has entries that can be read as the sides of 15 such triangles. That's over a thousand years before Pythagoras.

Nobody knows that Pythagoras proved it. No surviving Greek writing from the five centuries after his life credits him with it. The oldest proof that survives is Proposition 47 in Book I of Euclid's Elements.

Other cultures knew it independently. An Indian text, the Baudhayana Shulba Sutra, states the theorem, and in China it's called the Gougu theorem.