How to find the hypotenuse
In a right triangle, the hypotenuse is the longest side, opposite the right angle. By the Pythagorean theorem, c = √(a² + b²), where a and b are the two legs. For legs of 3 and 4, c = √(9 + 16) = √25 = 5. The last step is always a square root, which you can take on its own with the square root calculator.
How to use this calculator
Enter the lengths of the two legs (the sides that meet at the right angle). The result is the hypotenuse in the same unit. The two legs are interchangeable — order doesn't matter. To fill in the remaining sides and angles of the same triangle, use the right triangle calculator.
- Use the perpendicular sides only. If you enter the hypotenuse by accident, the answer will be too large.
- Keep units consistent — both legs in metres, or both in inches.
- Answers are often irrational. Legs of 1 and 1 give √2 ≈ 1.414, which the tool rounds for display.
Finding a leg instead
If you know the hypotenuse c and one leg a, the other leg is b = √(c² − a²). The classic whole-number triangles (3-4-5, 5-12-13, 8-15-17) are handy checks. For circle geometry, see the area of a circle calculator.
Frequently asked questions
- What is the formula for the hypotenuse?
- c = √(a² + b²), the square root of the sum of the squares of the two legs (the Pythagorean theorem).
- What is the hypotenuse of a 3-4-5 triangle?
- 5. Since 3² + 4² = 9 + 16 = 25, the hypotenuse is √25 = 5.
- How do I find a leg if I know the hypotenuse?
- Use b = √(c² − a²): subtract the known leg squared from the hypotenuse squared, then take the square root.
- Does this only work for right triangles?
- Yes. The Pythagorean theorem applies only to triangles with a 90° angle.
- Can the hypotenuse ever be shorter than a leg?
- No — it is always the longest side of a right triangle. If your result comes out smaller than one of the inputs, you have almost certainly entered the hypotenuse itself as a leg; use b = √(c² − a²) instead.