Pythagorean Theorem Calculator
Use Pythagoras' theorem to find a missing side of a right triangle.
About the Pythagorean Theorem Calculator
In any right-angled triangle, the square on the hypotenuse (the side opposite the right angle) equals the sum of the squares on the other two sides. Builders use the 3-4-5 rule to check corners are square.
The formula
a² + b² = c²
- c
- hypotenuse, the longest side
- a, b
- the two legs that meet at the right angle
Pythagorean triples
| a | b | c |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
| 7 | 24 | 25 |
| 20 | 21 | 29 |
| 9 | 40 | 41 |
Worked example
Example: Hypotenuse c = 6.4031242374
- Inputs: Find: Hypotenuse c; Leg a: 4; Leg b: 5.
- Formula: a² + b² = c²
- Square both legs and add 4² + 5² = 16 + 25 = 41
- Take the square root c = 6.4031242374
- Result: Hypotenuse c = 6.4031242374
Questions people ask
Does it work for any triangle?
Only right-angled ones. For others use the law of cosines.
How do I check a corner is square?
Measure 3 units along one side and 4 along the other; the diagonal should be exactly 5.