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Pythagorean Theorem Calculator

Enter any two sides of a right triangle to solve for the third using a² + b² = c².

a² + b² = c²

Fill in any two fields. Leave the unknown side blank.

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How to use the Pythagorean theorem calculator

Enter the values you know and leave the unknown blank. To find the hypotenuse, enter a and b: c = √(a² + b²). To find a leg, enter the other leg and the hypotenuse: a = √(c² − b²). The result shows the solved value and the formula used.

Pythagorean theorem reference

The theorem only applies to right triangles (triangles with a 90° angle). Common Pythagorean triples: 3-4-5, 5-12-13, 8-15-17, 7-24-25, 9-40-41. Multiply any triple by a constant to get another valid triple: 6-8-10, 9-12-15, etc.

FAQ

What is the Pythagorean theorem?

The Pythagorean theorem states that in any right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: a² + b² = c². It was known to ancient Babylonians and Greeks, and is attributed to the Greek mathematician Pythagoras.

What is a Pythagorean triple?

A Pythagorean triple is a set of three positive integers (a, b, c) that satisfy a² + b² = c². The most famous is 3-4-5: 9 + 16 = 25. These are useful in construction and engineering because they guarantee a perfect right angle.

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