Pythagorean Theorem Calculator
Find any side of a right triangle with the Pythagorean theorem. Pick the side to solve for and enter the other two. The calculator shows the missing side to up to 2 decimal places, so 3 and 4 give 5 and 1 and 1 give 1.41. To find a leg, the hypotenuse you enter has to be longer than the other leg.
a² + b² = c²
How to use the Pythagorean Theorem Calculator
- Enter your numbers in the Pythagorean Theorem Calculator above.
- Press the Calculate button to see the result.
- To try other numbers, change any value and press the button again.
The Pythagorean theorem
a² + b² = c² · · · where c is the hypotenuse (opposite the right angle)
Only works for right triangles. The hypotenuse is the longest side, opposite the 90° angle. The other two sides (legs) can be either a or b.
Worked example
A right triangle with legs 3 and 4: hypotenuse = √(9 + 16) = √25 = 5. The famous 3-4-5 right triangle. Given hypotenuse 13 and one leg 5: other leg = √(169 − 25) = √144 = 12.
Frequently asked questions
What is a Pythagorean triple?
A set of three positive integers a, b, c such that a² + b² = c². Common triples: (3,4,5), (5,12,13), (8,15,17), (7,24,25). Used in construction for squaring corners.
Does this work for non-right triangles?
No — only right triangles. For other triangles, use the Law of Cosines: c² = a² + b² − 2ab·cos(C), which generalizes the Pythagorean theorem (it becomes a² + b² when C = 90°).
How is this used in real life?
Construction (squaring foundations), navigation (distance), 2D graphics (distance between points), screen sizes (diagonal measurement from width and height).