Pythagorean Theorem Calculator
Find the missing side of a right triangle with a² + b² = c². Choose whether you're solving for the hypotenuse or a leg, enter the two known sides, and get the answer instantly.
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- 1Enter solve for in the form on the left.
- 2Fill in the remaining fields — the result updates automatically as you type.
- 3Review the highlighted result and the supporting breakdown on the right.
- 4Use Copy, Share or Print to save or send your result.
Why a² + b² = c² works
The Pythagorean theorem holds for every right triangle: the square of the hypotenuse equals the sum of the squares of the legs. Hundreds of proofs exist; the most intuitive ones rearrange four copies of the triangle inside a square to show the areas must balance.
Famous integer solutions — Pythagorean triples like (3, 4, 5), (5, 12, 13) and (8, 15, 17) — are handy for quick checks; builders still use the 3-4-5 rule to square corners.
Frequently Asked Questions
▸Does the Pythagorean theorem work for all triangles?
No, only right triangles. For other triangles use the law of cosines: c² = a² + b² − 2ab·cos(C), which reduces to the Pythagorean theorem when C is 90°.
▸What is a Pythagorean triple?
Three whole numbers satisfying a² + b² = c², like 3-4-5 or 5-12-13. Multiplying a triple by any whole number gives another triple.