a² + b² = c², solved in either direction
Find the hypotenuse from two legs, or a missing leg from one leg and the hypotenuse, plus the triangle's area and perimeter.
The theorem only holds for right-angled triangles, and it works both ways: square the two legs and add for the hypotenuse, or subtract to recover a missing leg.
It shows up far outside geometry class. Checking that a room is square, working out a screen's dimensions from its diagonal, or measuring a diagonal brace all come down to the same equation.
What this calculator shows
- The missing side, whether that is the hypotenuse or a leg
- The triangle's area and perimeter alongside it
- A clear error when the hypotenuse is shorter than a leg, which cannot happen
What to keep in mind
- Applies only to right-angled triangles — for any other triangle you need the law of cosines.
- The hypotenuse is always the longest side, so it must exceed either leg.
FAQs
How do I find a leg rather than the hypotenuse?
Subtract instead of adding: leg = √(c² − a²). Switch the mode above and enter the known leg and the hypotenuse.
What is a Pythagorean triple?
A set of three whole numbers that satisfy the theorem, like 3-4-5, 5-12-13 or 8-15-17. They are handy precisely because no decimals are involved.
Does this work for any triangle?
No, only right-angled ones. Without a 90° angle you need the law of cosines, which adds a term involving the angle between the sides.
How do I get a TV's width from its diagonal?
Use the aspect ratio as the leg proportions. For 16:9, a 55-inch diagonal works out to roughly 48 inches wide and 27 tall.
Worked example
Checking a corner is square
Input: Legs of 3 and 4
Output: Hypotenuse 5
Note: The 3-4-5 triangle is the builder's trick: measure 3 along one wall, 4 along the other, and if the diagonal is exactly 5 the corner is a true right angle.