Pythagorean Theorem Calculator
Enter any two sides to find the third. For the hypotenuse, use side c.
Please fill exactly two fields with positive numbers.
Check if Three Sides Form a Right Triangle
Pythagorean Theorem – a² + b² = c²
The Pythagorean theorem states that in any right-angled 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.
Famous Pythagorean Triples
A Pythagorean triple is a set of three positive integers that satisfy the theorem:
| a | b | c |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
| 7 | 24 | 25 |
| 9 | 40 | 41 |
| 6 | 8 | 10 |
Real-World Applications
- Construction – Checking corners are square using the 3-4-5 rule.
- Navigation – Finding straight-line distance between two points.
- Engineering – Calculating diagonal bracing lengths.
- Computer graphics – Distance calculations in 2D and 3D space.
Frequently Asked Questions
What is the hypotenuse?
The hypotenuse is the longest side of a right triangle, always opposite the 90° angle. It is denoted as c in the formula a²+b²=c².
Can the Pythagorean theorem be used in 3D?
Yes. For a 3D diagonal, the formula extends to d = √(x²+y²+z²), which is simply the theorem applied twice.
Who discovered the Pythagorean theorem?
Although named after the ancient Greek mathematician Pythagoras (c. 570–495 BC), the relationship was known to Babylonian and Indian mathematicians over a thousand years earlier.