Hypotenuse from two legs — with angles, perimeter and triple flagging.
One job, done fast: enter the two legs of a right triangle and get the hypotenuse. For finding a missing leg or solving from an angle, use the right triangle calculator instead.
Hypotenuse c
HypotenuseHow to use this tool
Enter the two legs (the sides that meet at the right angle) — not the hypotenuse. If you only know one leg and the hypotenuse, use the right triangle calculator instead.
The hypotenuse appears instantly, with the two acute angles, area and perimeter as extras, and the full working shown so you can check it.
Whole-number results such as 3-4-5 or 5-12-13 are flagged as Pythagorean triples.
Copy the result for homework, building plans or a quick check on site.
Formula & worked example
Worked example: legs 3 and 4 give hypotenuse √(3² + 4²) = √25 = 5, acute angles 36.87° and 53.13°, area 6 and perimeter 12. Another: legs 5 and 12 give hypotenuse 13, angles 22.62° and 67.38°, area 30 and perimeter 30. Legs 1 and 1 give √2 ≈ 1.4142, angles 45° and 45°, area 0.5 and perimeter ≈ 3.4142.
Limitations — read this before you rely on it
This tool assumes a right triangle: the two numbers you enter must be the legs meeting at the 90° angle. If your triangle is not right-angled, the answer will be wrong — use the general triangle calculator with the law of cosines instead. Both legs must be positive, and both must use the same unit, or the hypotenuse will be in a mixed-up unit too.
Frequently asked questions
A hypotenuse calculator finds the longest side of a right triangle from its two legs: c = √(a² + b²). Enter the legs and it also gives the two acute angles, area and perimeter as extras. It is deliberately single-purpose — for a missing leg or an angle-based solve, use the right triangle calculator.
Square each leg, add the squares, and take the square root. For legs 3 and 4: 3² + 4² = 9 + 16 = 25, and √25 = 5. That is the Pythagorean theorem.
A Pythagorean triple is a right triangle whose three sides are all whole numbers — 3-4-5, 5-12-13 and 8-15-17 are the most famous. This calculator flags one automatically when your legs and hypotenuse are all whole numbers.
Only for right triangles. In any other triangle the longest side is found with the law of cosines (c² = a² + b² − 2ab·cos C), which is what the general triangle calculator uses.
Yes — angle A (opposite leg a) is arctan(a ÷ b). For legs 3 and 4, arctan(3 ÷ 4) = 36.87°, and the other acute angle is 90° − 36.87° = 53.13°.