The Hypotenuse Calculator solves any right triangle from two known sides using
the Pythagorean theorem, a² + b² = c². Give it the two legs and it finds
the hypotenuse; give it the hypotenuse and one leg and it finds the other.
Finding the hypotenuse
The hypotenuse is the longest side, opposite the right angle. Its length is the square root of the sum of the squares of the other two sides:
c = √(a² + b²)
For legs of 3 and 4, c = √(9 + 16) = √25 = 5 — the classic 3-4-5 triangle.
Finding a missing leg
If you already know the hypotenuse and one leg, rearrange the formula:
a = √(c² − b²)
The known leg must be shorter than the hypotenuse. A hypotenuse of 13 with one
leg of 5 gives √(169 − 25) = √144 = 12 — the 5-12-13 triangle.
More than just the side
Alongside the missing length the tool returns both non-right angles (via the
arctangent of the opposite over adjacent side), the perimeter, and the area
½ × a × b. That makes it a complete right-triangle solver for geometry
homework, construction layout and any job where you need to square a corner.
Common Pythagorean triples
| a | b | c |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
| 7 | 24 | 25 |