Hypotenuse Calculator
The Longest Side, Solved Directly
In any right triangle, the hypotenuse is the side opposite the right angle — always the longest of the three — and it's fully determined by the two legs through one of the oldest results in mathematics. This calculator is a focused version of the Pythagorean relationship, built specifically for the single most common use case: given two legs, find the hypotenuse.
The Formula
c = √(a² + b²)
Both input sides (a and b) must be positive numbers, since a triangle can't have a leg of zero or negative length.
Common Applications
- Roofing and construction — finding rafter length from the horizontal run and vertical rise.
- TV and monitor sizing — a screen's advertised diagonal size is the hypotenuse of its width and height.
- Cable and wire runs — the shortest possible cable length between two points offset horizontally and vertically.
- Navigation — converting separate east-west and north-south displacement into straight-line distance.
| Side A | Side B | Hypotenuse |
|---|---|---|
| 6 | 8 | 10 |
| 5 | 12 | 13 |
| 9 | 12 | 15 |
How to Use This Calculator
- Enter Side A.
- Enter Side B.
- Select Calculate to see the hypotenuse and the worked formula.
Related Calculations
Need to solve for a leg instead of the hypotenuse, or work with the general form? The Pythagorean Theorem Calculator covers both directions. For angle-based right-triangle work, see the Sine Calculator.