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How to Use the Pythagorean Theorem

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) equals the sum of the squares of the other two sides: a² + b² = c². This fundamental geometric principle, discovered by Pythagoras, is used in construction, navigation, physics, and everyday measurements.

To find a missing side, enter the two known sides and leave one blank. The calculator solves for the missing value using the theorem. If you enter all three sides, it verifies whether they form a valid right triangle. The calculator also computes the triangle's area (½ × a × b) and perimeter (a + b + c).

Choose units for each side from millimeters to nautical miles. The calculator automatically converts between units and displays results in a common unit. This is useful when working with mixed measurements or different unit systems.

Right triangles appear in roofs, ramps, ladders, screen dimensions, and countless real-world applications. Use this calculator for homework, construction projects, or any situation requiring precise right triangle calculations.

Example

If side a = 3 cm and side b = 4 cm, then the hypotenuse c = 5 cm because 3² + 4² = 9 + 16 = 25 = 5². The area is 6 cm² and the perimeter is 12 cm.

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Frequently Asked Questions

The Pythagorean theorem states that in a right triangle, a² + b² = c², where c is the hypotenuse (longest side) and a and b are the other two sides. It's one of the most important formulas in geometry.
Enter the two shorter sides (a and b) and leave the hypotenuse (c) empty. The calculator computes c = √(a² + b²).
Yes. Enter the hypotenuse (c) and one other side (a or b). The calculator finds the missing side using a = √(c² − b²) or b = √(c² − a²).
Yes. Select any unit for each side. The calculator automatically converts and displays results in a common unit.
The calculator checks if the sides satisfy a² + b² = c². If not, it shows an error indicating the sides don't form a valid right triangle.