Pythagorean Theorem Calculator
The Pythagorean theorem links the three sides of a right triangle: a² + b² = c². Give it the two sides you know and it returns the missing hypotenuse or leg.
Your numbers
Result
- Side found
- Hypotenuse
- Formula used
- √(3² + 4²)
| Step | Detail |
|---|---|
| Finding | the hypotenuse |
| Formula | √(3² + 4²) |
| Result | 5 |
How the theorem works
In a right triangle, the square of the longest side (the hypotenuse, opposite the right angle) equals the sum of the squares of the other two sides: a² + b² = c². To find the hypotenuse, take √(a² + b²); legs 3 and 4 give √(9 + 16) = 5 — the classic 3-4-5 triangle.
Finding a missing leg
Rearrange the formula: a leg is √(c² − a²). If the hypotenuse is 5 and one leg is 3, the other is √(25 − 9) = 4. Switch the mode above to solve this way. The hypotenuse must always be the largest side, or the triangle cannot be right-angled.
Where it is used
Beyond the classroom, it is how you check a corner is square in construction (a 3-4-5 triangle guarantees a right angle), find a straight-line distance between two points, size a TV or screen diagonal, and cut rafters and braces. It only holds for right triangles.
Frequently asked questions
Sources
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