Pythagorean Theorem Calculator
Find a right triangle's hypotenuse from its two legs, or a missing leg from the hypotenuse and one known leg.
The Pythagorean Theorem
For any right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c². It's one of the oldest and most-used results in all of geometry.
Worked example
A right triangle with legs 6 and 8.
c² = 6² + 8² = 36 + 64 = 100
c = √100 = 10
Frequently Asked Questions
What is the Pythagorean theorem?
For any right triangle, a² + b² = c², where a and b are the two legs and c is the hypotenuse (the side opposite the right angle, always the longest side).
How do you find the hypotenuse?
Square both legs, add them together, then take the square root: c = √(a² + b²).
How do you find a missing leg instead of the hypotenuse?
Rearrange the formula: a = √(c² − b²). Subtract the known leg's square from the hypotenuse's square, then take the square root.
Does the Pythagorean theorem work on any triangle?
No — only right triangles, ones with exactly one 90° angle. For other triangles, use the Law of Cosines instead, which is a generalization that works for any triangle.
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