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Pythagorean Theorem Calculator
Use the Pythagorean theorem to find missing triangle sides. Calculate the hypotenuse from two sides, or find a missing side from the hypotenuse and one side.
Quick Facts
Most famous triple3-4-5
Discovered byPythagoras (~500 BCE)
Right angle90°
3D versiond = √(x² + y² + z²)
How to Use This Calculator
- Choose a mode: Find Hypotenuse or Find Missing Side.
- For hypotenuse: enter the two shorter sides (a and b).
- For missing side: enter the hypotenuse (c) and one known side.
- Click Calculate to see all three sides with a verification equation.
The Formula
a² + b² = c², where c is the hypotenuse (longest side). Find c: c = √(a² + b²). Find a: a = √(c² - b²). The theorem only applies to right triangles (one 90° angle).Frequently Asked Questions
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c². It was proven by the Greek mathematician Pythagoras around 500 BCE, though it was known to Babylonians much earlier.