Pythagorean Theorem Calculator
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Find a missing right-triangle side with a² + b² = c² — leave the unknown side at 0.
Right triangle sides
Leave the unknown side as 0 to solve for it.
Hypotenuse c
5
a = 3, b = 4, c = 5
- a² + b² = c²
- 9 + 16 = 25
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The Pythagorean theorem
The Pythagorean theorem relates the three sides of a right triangle: a² + b² = c², where c is the hypotenuse (the longest side, opposite the right angle) and a and b are the two legs. Given any two sides, you can always solve for the third.
To solve for the hypotenuse, add the squares of the two legs and take the square root: c = √(a² + b²). To solve for a leg, rearrange to a = √(c² − b²) (or the equivalent for b) — this only works when c is longer than the known leg.
Example: a 3-4-5 triangle is a classic right triangle. With legs a = 3 and b = 4, the hypotenuse is c = √(3² + 4²) = √25 = 5. Enter any two of the three sides and leave the third at 0 to solve for it.
Common questions
How do I tell the calculator which side to solve for?
Leave exactly one of the three side fields at 0 — the calculator solves for that side using the other two.
Does this only work for right triangles?
Yes. The Pythagorean theorem only applies to right triangles (one 90° angle). For other triangles, use the Law of Cosines or the triangle area calculator's Heron's formula mode.