How to Use Pythagoras' Theorem to Find a Missing Side
Pythagoras' theorem links the three sides of a right triangle in one simple equation. This guide shows how to rearrange it for any missing side.
What is the Pythagoras Calculator?
Choose which side is missing and enter the two sides you know. To find the hypotenuse, the tool takes the square root of the sum of the squares of the legs. To find a leg, it takes the square root of the hypotenuse squared minus the other leg squared, and it warns you if the hypotenuse is not longer than the known leg, since that cannot happen in a real triangle.
How to use it
- Choose which side you want to find.
- Enter the two sides you already know.
- Calculate to see the missing side.
Worked example
Finding the hypotenuse from legs 3 and 4 gives 5.
What is the hypotenuse of a right triangle with legs 3 and 4?
Square the legs to get 9 and 16, add them to get 25, and take the square root to get 5. So the hypotenuse is 5, which is why 3-4-5 is the most famous right-triangle example of all.
Frequently asked questions
Can the hypotenuse be shorter than a leg?
No. The hypotenuse is always the longest side of a right triangle, so if your numbers say otherwise, one of them must be wrong.
Does this work for triangles that are not right-angled?
No. Pythagoras only applies when one angle is exactly 90 degrees.