Pythagorean Theorem Calculator

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) equals the sum of the squares of the other two sides (legs): a² + b² = c². It only applies to right triangles.

A Pythagorean triple is a set of three positive integers that satisfy a² + b² = c². Common examples: (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25). Multiples of these also work, e.g. (6, 8, 10).

If you know the sides, use inverse trigonometric functions: angle A = arcsin(a/c) = arctan(a/b). Angle B = 90° - A since all angles sum to 180° and angle C = 90°.

The hypotenuse is the longest side of a right triangle, always opposite the 90-degree angle. It is always longer than either leg. In a = sqrt(c² - b²), c is the hypotenuse.

Yes, in 3D the space diagonal of a box with dimensions l, w, h is d = sqrt(l² + w² + h²), which is an extension of the 2D theorem applied twice (first to get the face diagonal, then to get the space diagonal).