Pythagorean Theorem Calculator

Find the missing side of a right triangle using the Pythagorean theorem.

Side A

Side B

Results

Hypotenuse (c)5

Triangle Area6

Perimeter12

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What is Pythagorean Theorem?

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides: a² + b² = c².

This is one of the most fundamental theorems in mathematics, used extensively in construction, navigation, physics, and engineering.

Formula

a² + b² = c² c = √(a² + b²) a = √(c² − b²)

Common Pythagorean triples: 3-4-5, 5-12-13, 8-15-17, 7-24-25

How to use this Pythagorean Theorem Calculator?

1. Enter Side A and Side B of the right triangle. 2. The calculator finds the hypotenuse. 3. Also shows area and perimeter.

Frequently asked questions

What is a Pythagorean triple?

A set of three positive integers (a, b, c) where a² + b² = c². Common examples: (3,4,5), (5,12,13), (8,15,17).

Does the Pythagorean theorem work for all triangles?

No, only for right triangles (those with a 90° angle). For other triangles, use the law of cosines.

How is the Pythagorean theorem used in real life?

Construction (checking if corners are square), navigation (finding shortest distance), screen sizes (diagonal from width and height), and architecture.

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