The Pythagorean Theorem is a fundamental relation in Euclidean geometry. It states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Formula & Calculation Method

The standard mathematical relationship used for this calculation is:

Hypotenuse: c = √(a² + b²); Side A: a = √(c² - b²); Side B: b = √(c² - a²)

Worked Step-by-Step Example

For a right triangle with sides a = 3 cm and b = 4 cm: c = √(3² + 4²) = √(9 + 16) = √25 = 5 cm.

How to Use

Identify the two sides of the right triangle you already know.
Enter their values in the input fields.
The calculator solves for the third missing side length automatically.

FAQ

Frequently Asked Questions

What is a Pythagorean triple?+

A Pythagorean triple consists of three positive integers (a, b, c) that satisfy the equation a² + b² = c². The most famous examples are (3, 4, 5) and (5, 12, 13).

Does the Pythagorean Theorem work on all triangles?+

No. The Pythagorean Theorem only applies to right-angled triangles (triangles containing a 90-degree angle). For non-right triangles, you must use the Law of Cosines.

Which side of the triangle is the hypotenuse?+

The hypotenuse is always the longest side of a right-angled triangle and is always situated directly opposite the 90-degree right angle.

How is the theorem used in construction?+

Builders use the theorem (specifically the 3-4-5 rule) to ensure corners are perfectly square (90 degrees). By measuring 3 feet along one wall and 4 feet along another, the diagonal distance between those points must be exactly 5 feet if the corner is square.