The Pythagorean theorem is arguably the most-used result in all of geometry: in any right triangle, the square on the hypotenuse equals the sum of the squares on the two legs. Builders, navigators, and screen manufacturers all rely on it daily.
Cómo funciona
Enter the two legs (the sides forming the right angle). The calculator squares them, sums, and takes the square root for the hypotenuse — and also returns the triangle's area and perimeter as a bonus.
La fórmula
a and b are the legs, c the hypotenuse (always the longest side). Area = a×b ÷ 2; perimeter = a + b + c.
Ejemplo resuelto
Legs of 3 and 4: c = √(9 + 16) = √25 = 5 — the famous 3-4-5 triangle, used since antiquity to lay out perfect right angles with a knotted rope.
Preguntas frecuentes
How do I find a leg when I know the hypotenuse?
Rearrange: a = √(c² − b²). A 10-meter ladder (hypotenuse) with its base 6 m from the wall reaches √(100 − 36) = 8 m up.
Does the theorem work on non-right triangles?
No — it's exclusive to right triangles. For others use the law of cosines, c² = a² + b² − 2ab·cos(C), which reduces to Pythagoras exactly when C = 90°.
What are Pythagorean triples?
Whole-number solutions like (3,4,5), (5,12,13), (8,15,17) — and every multiple of them, such as (6,8,10). Handy for quick mental checks and construction layouts.