Pythagoras Hypotenuse
Calculator
Results
- Hypotenuse
- 5
- Area
- 6
- Perimeter
- 12
Results
| Hypotenuse | 5 |
| Area | 6 |
| Perimeter | 12 |
formula-map diagram
- Hypotenuse
- 5
- Area
- 6
- Perimeter
- 12
Formula map
Formula
c = √(a² + b²)= 5
Note
Simplified model: these are exact results of the stated idealised formulas, assuming perfect shapes and exact inputs. Real measurements carry error, and the ellipse perimeter is a Ramanujan approximation. Verify independently before relying on these figures.
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See all →Frequently asked questions
What does this calculator find?+
The length of the hypotenuse (the longest side) of a right triangle, given the lengths of the two legs (the sides forming the right angle).
What is the actual formula?+
The Pythagorean theorem: c² = a² + b², so the hypotenuse c equals the square root of (a² + b²), where a and b are the two legs.
Does this only work for right triangles?+
Yes, the Pythagorean theorem strictly applies only when there is a genuine 90-degree angle between the two given sides. For any other triangle you need the law of cosines instead.
Can I use this to find a leg instead of the hypotenuse?+
If you know the hypotenuse and one leg, rearrange the formula to a = √(c² - b²). Some calculators offer this as a separate mode — check whether the tool lets you solve for a missing leg.
Why is the hypotenuse always the longest side?+
Because it sits opposite the largest angle in the triangle (the 90-degree angle), and in any triangle the longest side is always opposite the largest angle.