Pythagorean theorem calculator

Created by

Narendra Kumar

Verified by

Reema Singh

Last Updated: 23-04-2026

Pythagorean Theorem: Definition, Formula and Example

The Pythagorean theorem is a fundamental rule in geometry that explains the relationship between the three sides of a right-angled triangle. A right triangle contains one angle equal to 90°. The longest side of the triangle is called the hypotenuse, while the other two sides are called legs.

The theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides of the triangle.

Right Triangle Graph Explanation

A right triangle can be visualized on a coordinate plane. Suppose we place the triangle with the following points:

• Point O (0,0) forms the right angle
• Point A (a,0) represents the horizontal side
• Point B (0,b) represents the vertical side

The line connecting points A and B forms the hypotenuse. The horizontal and vertical sides correspond to the values a and b. The triangle angles always add up to 180°, with one angle fixed at 90°.

Example of the Pythagorean Theorem

Consider a right triangle with the following sides:

• Side a = 3
• Side b = 4

Apply the formula:

Calculate the squares:

Take the square root:

This triangle is known as the 3-4-5 right triangle, one of the most common examples used to explain the Pythagorean theorem.

Applications of the Pythagorean Theorem

The Pythagorean theorem is widely used in many practical situations and scientific fields. Some common applications include:

• Calculating distances in coordinate geometry
• Construction and building measurements
• Architecture and engineering design
• Computer graphics and game development
• Navigation and GPS distance calculations

Because of its simplicity and usefulness, the Pythagorean theorem remains one of the most important formulas in mathematics and geometry.