Pythagorean theorem calculator
The missing side of a right triangle from the other two, using a² + b² = c².
About this calculator
This Pythagorean theorem calculator finds the missing side of a right triangle. Enter the two shorter sides to get the hypotenuse, or the hypotenuse and one side to get the other.
It also shows the two angles, the area and the perimeter, and the check that a² + b² = c².
How it works
In a right triangle, a² + b² = c², where c is the hypotenuse, the side opposite the right angle. So c = √(a² + b²), and a missing shorter side is √(c² − a²).
Last reviewed:
Worked example
- Find: The hypotenuse
- Side a: 3
- Side b: 4
Hypotenuse c: 5
Common questions
What is the hypotenuse?
The longest side of a right triangle, opposite the 90° angle. It's always c in a² + b² = c².
Does the Pythagorean theorem work for every triangle?
Only for right triangles. For other triangles, use the law of cosines, or the triangle calculator if you know all three sides.
What is a Pythagorean triple?
Three whole numbers that fit the theorem, such as 3, 4, 5 or 5, 12, 13. Builders use 3-4-5 to check that a corner is square.
The story behind it
Where the idea came from: A Babylonian clay tablet known as Plimpton 322, from about 1800 BC, lists sets of numbers that fit a² + b² = c², more than a thousand years before Pythagoras.
The rule is named after the Greek thinker Pythagoras, but it was known in Babylon, India and China long before. The Greeks were among the first to prove it holds for every right triangle. It is still one of the most used results in maths, from building to navigation.
Why you can trust this calculator
- It runs in your browser. Nothing you type into it is sent anywhere.
- The method is explained on this page, so you can check it yourself.
- Free to use, with no sign-up.
- Results are estimates, so please double-check anything important.
- Spotted a mistake? Tell us and we'll look into it.
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