Right Triangle Calculator · Practical guide
How to Find the Hypotenuse of a Right Triangle
Square the two legs, add them, and take the square root — the Pythagorean theorem does the rest.
At a glance
The Pythagorean Method
When you know both legs, the hypotenuse is c = √(a² + b²). For legs of 3 and 4: √(9 + 16) = √25 = 5. For legs of 5 and 12: √(25 + 144) = √169 = 13. The hypotenuse is always the longest side, sitting opposite the 90° angle, so any answer shorter than a leg signals an arithmetic slip.
Interactive tool
Right Triangle Calculator
Enter your own values, then compare the result with the examples below.
Right Triangle Solution
Common Pythagorean Triples
Some leg pairs produce whole-number hypotenuses. Recognizing these triples saves calculation time — and scaled versions (6-8-10 is just 3-4-5 doubled) work identically.
| Leg A | Leg B | Hypotenuse |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
| 7 | 24 | 25 |
| 20 | 21 | 29 |
| 9 | 40 | 41 |
When You Know a Leg and an Angle Instead
If you have one leg and the angle opposite or adjacent to it, use trigonometry: c = a ÷ sin(A) when side a is opposite angle A. For example, a leg of 6 opposite a 30° angle gives c = 6 ÷ 0.5 = 12. If the known leg is adjacent to the angle, use c = a ÷ cos(A) instead.
When You Know the Hypotenuse and One Leg
Rearrange the theorem to solve for the missing leg: b = √(c² − a²). A hypotenuse of 13 with one leg of 5 gives √(169 − 25) = √144 = 12. Enter any two known values in the calculator above and it solves the full triangle — remaining sides, both acute angles, area, and perimeter.
Frequently Asked Questions
Does the Pythagorean theorem work for all triangles?
No, it applies only to right triangles — those containing one 90° angle. For other triangles you need the law of cosines or law of sines.
Can the hypotenuse ever equal a leg?
No. The hypotenuse is strictly the longest side of a right triangle because c² = a² + b² means c is always greater than either leg alone.
What if my legs give a hypotenuse that is not a whole number?
That is normal — most leg pairs produce irrational hypotenuses. Legs of 1 and 1 give √2 ≈ 1.4142, and legs of 2 and 3 give √13 ≈ 3.6056.
How do I find the hypotenuse of a 45-45-90 triangle?
Multiply the leg by √2 ≈ 1.4142. A leg of 10 gives a hypotenuse of about 14.1421, since both legs are equal in an isosceles right triangle.