Enter the two legs of a right triangle to find the hypotenuse.
The right triangle rule
The Pythagorean theorem links the three sides of a right triangle: the square of the hypotenuse equals the sum of the squares of the two shorter sides. It applies only to triangles with a ninety degree angle, where the hypotenuse is the longest side, opposite that angle.
It is one of the most practical results in all of mathematics, used to check square corners in construction, measure straight line distances, and underpin coordinate geometry. Whole number sets that satisfy it, such as three, four, five, are called Pythagorean triples.
The formula
Worked example
Legs of 3 and 4 give a hypotenuse of sqrt(9 + 16) = sqrt(25) = 5.
How to read your result
The theorem holds only for right triangles. The hypotenuse is always the longest side and sits opposite the right angle.
Frequently asked questions
- Does this work for any triangle?
- No, only right triangles with a 90 degree angle.
- What is a Pythagorean triple?
- A set of whole numbers that fit the theorem, such as 3, 4, 5.
- Can I find a leg instead?
- Rearrange the formula: a leg equals the square root of the hypotenuse squared minus the other leg squared.
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