What the theorem says
In every right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the legs: c² = a² + b². The hypotenuse is always the longest side, and the theorem only holds when one angle measures exactly 90°.
How to find the missing side
If you know both legs, the hypotenuse is c = √(a² + b²). If you know the hypotenuse and one leg, the other leg is b = √(c² − a²). The calculator handles both cases and also shows the triangle's area and perimeter.
Pythagorean triples and distance between points
When all three sides are whole numbers that satisfy the theorem, like 3, 4, 5 or 5, 12, 13, they form a Pythagorean triple. The same idea measures the distance between two points (x1, y1) and (x2, y2): it is the hypotenuse of a triangle whose legs are the differences in x and in y.
Practical example
A 5 m ladder leaning with its base 3 m from the wall reaches 4 m up, since 5² − 3² = 4². The diagonal of a 12 m by 5 m room is 13 m, because √(12² + 5²) = 13.