Pythagorean Theorem Calculator
Find the hypotenuse, area, and perimeter of a right triangle.
Try an example
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About this calculator
How This Pythagorean Theorem Calculator Works
Enter the lengths of the two legs of a right triangle, and the calculator returns the hypotenuse, the triangle's area, and its perimeter.
Worked Example
For legs of 3 and 4, the hypotenuse is 5 — the classic 3-4-5 right triangle — with an area of 6 and a perimeter of 12.
The Formula
a² + b² = c², so c = √(a² + b²). This relationship holds for every right triangle (one with a 90° angle) — it's one of the oldest and most widely used theorems in geometry, named for the ancient Greek mathematician Pythagoras, though evidence of the relationship predates him in other civilizations.
Common Real-World Uses
- Construction and carpentry — checking that a corner is truly square, or finding the length of a diagonal brace
- Finding a straight-line distance — the shortest path between two points that differ in both horizontal and vertical position
- Ladder safety — figuring out how far a ladder's base needs to be from a wall to safely reach a given height
Note this only works for right triangles. For a triangle without a right angle, use the Law of Cosines instead, on the Triangle Calculator.
Worked example
For legs a = 3 and b = 4, the hypotenuse is c = √(9 + 16) = 5 — the classic 3-4-5 right triangle, with an area of 6.
Frequently asked questions
Does this work for any triangle?
No — the Pythagorean theorem only applies to right triangles (one 90° angle). For a triangle without a right angle, use the Law of Cosines instead, available on the Triangle Calculator.
Can I solve for a leg instead of the hypotenuse?
This calculator solves for the hypotenuse given both legs. To solve for a missing leg given the hypotenuse and one leg, rearrange the formula: a = √(c² − b²).
What's a real-world use for this?
Common uses include finding the diagonal of a rectangle, the length of a brace or ladder against a wall, or the straight-line distance between two points on a grid.