Find the hypotenuse or side dimensions using the Pythagorean theorem.
The Pythagorean Theorem Calculator is a coordinate and triangle tool designed to solve for any missing side of a right-angled triangle. Named after the ancient Greek mathematician Pythagoras, the theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides: a² + b² = c².
The calculator can solve for any side length given the other two: - **Hypotenuse (c):** c = √(a² + b²) - **Side (a):** a = √(c² − b²) - **Side (b):** b = √(c² − a²) A set of three integer side lengths that satisfy the theorem is called a Pythagorean triple, such as (3, 4, 5) or (5, 12, 13).
The Pythagorean theorem is used extensively in construction and carpentry to verify if a corner is a perfect 90-degree angle (using the 3-4-5 rule). It is also key in navigation to calculate straight-line distances and in computer graphics to scale vectors. The Pythagorean calculator provides fast, exact radical and decimal outputs, helping users plan layouts, check angles, and complete math assignments.
Pythagorean Theorem
In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs.
How it Works & Formula
Calculates the length of any side of a right-angled triangle using the Pythagorean theorem.
Practical Examples
If walls are 6m and 8m, diagonal must be √(6² + 8²) = 10m to be perfectly square.
Frequently Asked Questions
What is a Pythagorean triple?
A set of three positive integers (a, b, c) that fit the equation a² + b² = c², such as (3, 4, 5) or (5, 12, 13).