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Pythagorean Theorem Calculator
Solve for any side of a right triangle — a² + b² = c²
Pythagorean Theorem FAQ
What is the Pythagorean theorem?
The Pythagorean theorem states that in any right triangle (a triangle with a 90° angle), 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 was named after the ancient Greek mathematician Pythagoras.
Which side is the hypotenuse?
The hypotenuse is always the longest side and is always opposite the right angle (90° angle). In the formula a² + b² = c², c is the hypotenuse. You can never use the Pythagorean theorem to find the hypotenuse if you don't know which angle is 90°.
What are Pythagorean triples?
Pythagorean triples are sets of three positive integers that satisfy a² + b² = c². The most famous is 3-4-5. Any multiple of a triple is also a triple (6-8-10, 9-12-15, etc.). They're useful for checking your work — if your answer is one of these, the triangle is likely correct.
Does the Pythagorean theorem work for all triangles?
No — only right triangles. For non-right triangles, you need the Law of Cosines: c² = a² + b² − 2ab·cos(C), which generalizes the Pythagorean theorem. When angle C = 90°, cos(90°) = 0 and it reduces back to a² + b² = c².