Pythagorean Theorem Calculator
Solve for any side of a right triangle using the Pythagorean theorem.
The Pythagorean Theorem
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides, called legs. It is written as a² + b² = c², where a and b are the legs and c is the hypotenuse.
To find the hypotenuse: c = √(a² + b²). To find a leg when the hypotenuse and the other leg are known: a = √(c² − b²).
Identifying the Hypotenuse
The hypotenuse is always the longest side of a right triangle and lies directly opposite the 90-degree angle. The two shorter sides that form the right angle are the legs. When solving for a leg, the hypotenuse you enter must be longer than the known leg — otherwise the triangle cannot exist.
Common Pythagorean Triples
A Pythagorean triple is a set of three positive integers that satisfy a² + b² = c². These appear often in geometry problems:
- 3, 4, 5 — the most common triple (3² + 4² = 5²)
- 5, 12, 13
- 8, 15, 17
- 7, 24, 25
- Any multiple of a triple is also a triple, such as 6, 8, 10 (double of 3, 4, 5).