What is the Pythagorean Theorem?

The Pythagorean theorem states that in any right triangle with legs a and b and hypotenuse c, the sum of the squares of the two legs equals the square of the hypotenuse: a² + b² = c².

What is a Pythagorean Triple?

A Pythagorean triple consists of three positive integers (a, b, c) such that a² + b² = c². Famous examples include (3, 4, 5), (5, 12, 13), and (8, 15, 17).

Pythagorean Theorem Calculator — Solve a² + b² = c²

The Pythagorean Theorem (a² + b² = c²)

Attributed to the ancient Greek mathematician Pythagoras (c. 570–495 BC) and independently discovered by ancient Indian mathematicians in the Baudhayana Sulba Sutras (c. 800 BC), this theorem establishes the fundamental relationship between the three sides of any right-angled Euclidean triangle.

Frequently Asked Questions

Can the hypotenuse be shorter than a leg?

No. In any right triangle, the hypotenuse is opposite the 90-degree right angle (the largest angle in the triangle) and is always the strictly longest side.

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