Can I use this calculator to find sides 'a' or 'b'?

This calculator is specifically designed to find the hypotenuse (side 'c'). To find a missing leg ('a' or 'b'), you would need to rearrange the formula to a = sqrt(c² - b²) or b = sqrt(c² - a²). We may add this functionality in the future!

Does it work for any triangle?

No, the Pythagorean theorem and this calculator only apply to right-angled triangles (triangles with one 90-degree angle).

What is a Pythagorean triple?

A Pythagorean triple is a set of three positive integers (a, b, c) that perfectly satisfy the theorem, such as (3, 4, 5), (5, 12, 13), or (8, 15, 17). If you enter two integers from a triple, the result for the hypotenuse will also be a clean integer.

Pythagorean Theorem Calculator

Easily calculate the length of the hypotenuse of a right-angled triangle.

Calculate Hypotenuse (c)

Side A

Side B

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About the Pythagorean Theorem

Learn about this fundamental geometric theorem and its applications.

What is the Pythagorean Theorem?

The Pythagorean theorem is a fundamental principle in Euclidean geometry that describes the relationship between the three sides of a right-angled triangle. It states that the square of the hypotenuse (the side opposite the right angle, denoted as 'c') is equal to the sum of the squares of the other two sides (the legs, denoted as 'a' and 'b').

a² + b² = c²

This calculator uses this timeless formula to quickly find the length of the hypotenuse when you provide the lengths of the other two sides. It is one of the most important concepts in basic geometry and has wide-ranging applications.

How to Use This Calculator

To find the length of the hypotenuse (side 'c'), simply enter the lengths of the other two sides of the right-angled triangle, 'a' and 'b', into the input fields. Then, click the "Calculate" button. The calculator will instantly solve for 'c' using the Pythagorean theorem.

Frequently Asked Questions

Practical Applications

This theorem is not just for math class; it has many real-world uses:

Architecture and Construction: Architects and builders use it to calculate the required length of support beams or to ensure that corners are perfectly square (90 degrees). For example, finding the diagonal length of a room.
Navigation: It can be used to find the shortest distance between two points on a map (as the crow flies). For instance, calculating the distance a helicopter travels between two points.
DIY Projects: Determining the length of a ladder needed to reach a certain height on a wall, or finding the dimensions for a sloped roof.
Surveying: Surveyors use it to determine the height of buildings and mountains from a distance.