Pythagorean Theorem Calculator
Find the missing side of a right triangle or check if three sides form a right triangle. Visual SVG diagram with step-by-step working
Enter any 2 sides to find the missing one
Enter 2 sides to find the missing one
How the Pythagorean Theorem Works
For a right-angled triangle: a² + b² = c², where c is the hypotenuse (longest side, opposite the right angle) and a, b are the other two sides. Given any two sides, you can find the third. So for legs of 3 and 4: c² = 9 + 16 = 25, c = 5. The classic 3-4-5 triangle is the smallest integer right triangle.
Used everywhere in geometry, construction, navigation, computer graphics. To find the diagonal of a rectangular room: a = length, b = width, c = diagonal. A 3m × 4m room has a 5m diagonal. To check if a corner is square (90°): measure 3 ft from corner along one wall, 4 ft along the other - the distance between those points should be exactly 5 ft if the corner is square.
Common Pythagorean Triples
| a | b | c (hypotenuse) |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 6 | 8 | 10 |
| 7 | 24 | 25 |
| 8 | 15 | 17 |
| 9 | 40 | 41 |
| 12 | 16 | 20 |
| 20 | 21 | 29 |
Frequently Asked Questions
Why are these called 'triples'?
Sets of three integers (a, b, c) where a² + b² = c². The smallest is (3, 4, 5). Multiples of any triple are also triples (6, 8, 10 = 2 × the 3-4-5 triple). 'Primitive triples' are the simplest forms - (3,4,5), (5,12,13), (8,15,17) - that aren't multiples of smaller triples.
How do I find the third side?
If you know c and a: b² = c² - a², so b = √(c² - a²). If you know a and b: c = √(a² + b²). Always remember c is the longest side (hypotenuse). Square root is the operation; result is the side length.
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