Pythagorean theorem calculator
Right triangle solver: find the hypotenuse from two legs, or a missing leg from the hypotenuse, with the angles, area and working.
See why a² + b² = c²
Build a square on each side of the right triangle. The theorem says the two smaller squares together hold exactly as many unit tiles as the big one. Change the legs and count.
Pythagorean triples
Whole-number right triangles. Any multiple of a triple is also a triple (6-8-10, 9-12-15), which is why builders use them to check corners are square.
| a | b | c |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
| 7 | 24 | 25 |
| 20 | 21 | 29 |
| 9 | 40 | 41 |
Show me the steps
An AI tutor walks through the working for this exact result. The answer above is computed in your browser; the explanation is optional and is the only thing that leaves your device.
Right triangle: find the hypotenuse c given a = 3, b = 4 = a = 3, b = 4, c = 5
Questions people ask
What is the Pythagorean theorem?
In a right triangle, 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.
How do I find a missing leg?
Rearrange to a = √(c² − b²). Choose “Find leg a” or “Find leg b” above. The hypotenuse must be the longest side, otherwise no right triangle exists.
Does it work for triangles without a right angle?
No. For other triangles, use the law of cosines, c² = a² + b² − 2ab·cos C, which the triangle calculator applies for you.
How can I check if a corner is square?
The 3-4-5 rule: measure 3 units along one side and 4 along the other; if the diagonal between those points is exactly 5, the corner is 90°. Builders use multiples like 6-8-10 or 9-12-15 feet.