Pythagorean Theorem Calculator

About the Pythagorean Theorem Calculator

The Pythagorean Theorem states that in any right-angled triangle, the square of the length of the hypotenuse (c)—the side opposite the 90° right angle—is equal to the sum of the squares of the other two legs (a and b).

This calculator finds the exact hypotenuse length, radical form, triangle area, and perimeter from any two right-triangle legs.

Pythagorean Theorem & Right Triangle Formulas

For a right triangle with legs a, b and hypotenuse c:

How to Find the Hypotenuse of a Right Triangle

1. Square Both Legs: Calculate a² and b².
2. Add the Squares Together: Compute the sum a² + b².
3. Take the Square Root: Find √(a² + b²) to obtain the hypotenuse c.

Worked Example: For a right triangle with legs a = 3 and b = 4, c² = 3² + 4² = 9 + 16 = 25. Taking the square root gives c = √25 = 5.

Frequently Asked Questions (FAQ)

What is a Pythagorean triple?

A Pythagorean triple is a set of three positive whole integers (a, b, c) that satisfy a² + b² = c², such as (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).