Pythagorean Theorem Calculator
Find the hypotenuse from the two legs, or a leg when you know the hypotenuse and the other leg. With the formula and every step shown.
Formula: c = √(a² + b²)
Steps:
The result uses the same unit as the sides you entered (inches, feet, cm — anything works); the area is in that unit squared.
How the Pythagorean theorem works
In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: c² = a² + b². Rearranging gives the two formulas this calculator uses: the hypotenuse is c = √(a² + b²), and a missing leg is b = √(c² − a²). Keep in mind it only applies to right triangles — those with a 90° angle — and the hypotenuse is always the longest side, which is why the tool warns you if you enter a leg longer than the hypotenuse.
The 3-4-5 rule and other real-world uses
The 3-4-5 triple (and its multiples 6-8-10, 9-12-15…) has been used by builders and carpenters for centuries to lay out a perfect right angle without a square: measure 3 units along one side and 4 along the other — if the diagonal is exactly 5, the corner is 90°. The theorem also gives you the diagonal of a TV or monitor (the advertised inches are literally the screen's hypotenuse), how high a ladder reaches when leaned against a wall, and the diagonal of a room or a rectangular lot.