Pythagorean Theorem Calculator

Calculate the missing side of a right triangle using the Pythagorean theorem (a² + b² = c²).

Solve For

a² + b² = c²

Side a

Side b

How to Use the Pythagorean Theorem Calculator

Select which side you want to find — the hypotenuse (c) or one of the legs (a or b). Enter the two known values and the calculator will instantly compute the missing side. The visual diagram updates to show the triangle with your values.

Real-World Applications

The Pythagorean theorem is used in construction (ensuring corners are square), navigation (calculating distances), architecture, engineering, and computer graphics. It is one of the most fundamental formulas in mathematics and geometry.

Frequently Asked Questions

What is the Pythagorean theorem?

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides: a² + b² = c².

How do I find the hypotenuse?

Enter the lengths of sides a and b, and the calculator will compute c = √(a² + b²). For example, if a = 3 and b = 4, then c = √(9 + 16) = √25 = 5.

Can I find a missing leg instead of the hypotenuse?

Yes. If you know the hypotenuse (c) and one leg (a), you can find the other leg: b = √(c² - a²). Select 'Find side a' or 'Find side b' mode in the calculator.

What are Pythagorean triples?

Pythagorean triples are sets of three positive integers that satisfy a² + b² = c². Common examples include (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25). Any multiple of a triple is also a triple.