What is a Pythagorean triple?
A Pythagorean triple consists of three positive integers (a, b, c) that satisfy a² + b² = c² exactly, such as (3, 4, 5) or (5, 12, 13).
Does the Pythagorean theorem apply to all triangles?
No. The theorem applies strictly to right-angled triangles with a 90° angle. For non-right triangles, you must use the generalized Law of Cosines: c² = a² + b² - 2ab cos(C).
How do carpenters use the 3-4-5 rule?
Carpenters measure 3 feet along one wall and 4 feet along an adjacent wall. If the diagonal between them is exactly 5 feet, the corner forms a perfect 90° square angle.
Can the hypotenuse ever be shorter than either leg?
No. The hypotenuse is opposite the largest (90°) angle and is always the strictly longest side in any right triangle.
Can side lengths be decimals?
Yes. The calculator works seamlessly with any positive real numbers or decimals.
How accurate is the result?
Results use JavaScript's 64-bit floating point — accurate to 15+ significant digits for most calculations.
Can I enter decimal numbers?
Yes, decimals are fully supported.
Is it free?
Yes, completely free.
Does it show the formula?
Yes, the formula is displayed on the page.
Can I use it on mobile?
Yes, the calculator is fully responsive.
Does it save my inputs?
No data is stored — all calculations are done locally in your browser.
What if I get an error?
Check for invalid inputs such as division by zero or negative square roots.