What are Pythagorean triples?

Pythagorean triples are integer solutions to a² + b² = c². The simplest are 3-4-5, 5-12-13, 8-15-17, and 7-24-25. Any multiple of a triple is also a triple (e.g. 6-8-10).

How do I find a missing leg?

If you know the hypotenuse c and one leg a: b = √(c² - a²). For example, if c = 5 and a = 3: b = √(25 - 9) = √16 = 4.

When is the Pythagorean theorem used in real life?

It is used by builders and architects for squaring corners, by engineers for structural analysis, in GPS/navigation (distances on a grid), and in computer graphics (pixel distances).

Pythagorean Theorem Calculator

The Pythagorean Theorem Calculator finds the hypotenuse (c) of a right triangle when you know both legs (a and b), using the formula a² + b² = c². You can also find a missing leg by entering the hypotenuse and one leg. This is one of the most fundamental theorems in geometry, used in architecture, engineering, navigation, and everyday measurement.

Side a (leg)

Side b (leg)

How to Use This Calculator

1
Enter the length of side a (one leg of the right triangle).
2
Enter the length of side b (the other leg).
3
Click Calculate to find the hypotenuse c.
4
To find a missing leg, rearrange: a = √(c² - b²).

Frequently Asked Questions

In a right-angled triangle, the square of the hypotenuse equals the sum of squares of the other two sides: a² + b² = c², where c is the hypotenuse (the longest side, opposite the right angle).

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