Pythagorean Theorem Calculator

For a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: a squared plus b squared equals c squared, where c is the side opposite the right angle.

Rearrange the formula. A leg equals the square root of the hypotenuse squared minus the other leg squared, so a = sqrt(c squared minus b squared). The hypotenuse must be longer than the leg you already know.

The hypotenuse sits opposite the right angle and is always the longest side of a right triangle. If you try to solve a leg with a hypotenuse that is shorter than the known leg, no real triangle exists and the tool flags it.

Because the two legs meet at the right angle, the area is half their product: area = a times b divided by 2. The perimeter is simply the three sides added together, a + b + c.

No. You can enter any positive decimals. Whole-number sets like 3-4-5 or 5-12-13 are called Pythagorean triples, but most right triangles have at least one irrational side, such as a = b = 1 giving c = sqrt(2).

No. The calculation runs entirely in your browser, so the numbers you type are never uploaded or stored.