a² + b² = c²
The Pythagorean theorem says that in a right triangle the square of the hypotenuse (the longest side, opposite the right angle) equals the sum of the squares of the other two sides. It is one of the most useful results in geometry.
Choose which side you want to find and enter the other two. The calculator solves for the hypotenuse or a missing leg and also gives the area, perimeter, both acute angles and whether the sides form a whole-number Pythagorean triple.
How it is calculated
Worked example
Legs 3 and 4
- Hypotenuse
- 5
- Area
- 6
- Perimeter
- 12
- Angles
- 36.87° and 53.13°
3, 4, 5 is the best-known Pythagorean triple. Others include 5, 12, 13 and 8, 15, 17.
Where it helps
- Checking that a corner is square: a 3-4-5 layout gives a perfect right angle on a building site.
- Finding the length of a ladder, ramp or diagonal brace.
- The diagonal of a screen or a rectangle is its hypotenuse.
Beyond right triangles
This same relationship extends directly into 3D: the diagonal of a rectangular box is found the same way, by combining the squares of all three edges and taking the square root — which is exactly how this site's distance calculator works out the distance between two points in 3D space.