How to Find the Hypotenuse (Pythagorean Theorem)
The hypotenuse is the longest side of a right triangle — the one opposite the right angle. The Pythagorean theorem connects it to the other two sides with one of the most famous formulas in maths.
The formula
For a right triangle with legs a and b and hypotenuse c: a² + b² = c². To find the hypotenuse, take the square root of the sum: c = √(a² + b²).
A worked example
A triangle has legs of 3 and 4. c = √(3² + 4²) = √(9 + 16) = √25 = 5. The 3-4-5 triangle is the classic example because every side is a whole number.
Another common one is 5-12-13: √(25 + 144) = √169 = 13.
Finding a leg instead
You can rearrange the same formula to find a missing leg when you already know the hypotenuse: a = √(c² − b²). Just make sure c (the hypotenuse) is always the largest value.
Calculate it instantly
Enter the two legs into the Pythagorean Theorem Calculator to get the hypotenuse (and the triangle’s area). For circles and their measurements, the Circle Calculator is a handy companion.
Related tools
Last updated: July 6, 2026