How the Pythagorean theorem works
The Pythagorean theorem applies to right-angled triangles. It says the square of the longest side (the hypotenuse) equals the sum of the squares of the other two sides. Given the two shorter sides, you can always find the hypotenuse.
The formula
a squared + b squared = c squared, so c = the square root of (a squared + b squared).
Worked example
With sides of 3 and 4: 3 squared is 9, 4 squared is 16, and 9 + 16 = 25. The square root of 25 is 5, so the hypotenuse is 5. This is the famous 3-4-5 triangle.
Frequently asked questions
What is the Pythagorean theorem?
For a right triangle, a squared plus b squared equals c squared, where c is the hypotenuse. It links the three side lengths.
Can I find a shorter side instead?
Yes, by rearranging: a = the square root of (c squared minus b squared). This calculator finds the hypotenuse from the two legs.
What is a 3-4-5 triangle?
A right triangle whose sides are 3, 4 and 5. It is the simplest whole-number example of the theorem.