Pythagorean Theorem Calculator

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: a² + b² = c². It only applies to right triangles — triangles with one 90-degree angle.

Square both legs, add them together, then take the square root: c = √(a² + b²). For example, with legs of 3 and 4: c = √(9 + 16) = √25 = 5. This is the famous 3-4-5 right triangle.

Rearrange the theorem: a = √(c² − b²). Subtract the square of the known leg from the square of the hypotenuse, then take the square root. The hypotenuse must always be the longest side, so c² − b² must be positive.

Pythagorean triples are whole-number side lengths that satisfy the theorem. The most common are 3-4-5, 5-12-13, 8-15-17, and 7-24-25. Any multiple of a triple is also a triple, such as 6-8-10 (the 3-4-5 triple doubled).

No — it only works for right triangles. For triangles without a right angle, use the Law of Cosines, which is a generalization: c² = a² + b² − 2ab·cos(C). When angle C is 90 degrees, cos(C) = 0 and it reduces to the Pythagorean theorem.