Distance Calculator

About Distance Calculation

The distance formula is a direct application of the Pythagorean theorem. In 2D, the horizontal and vertical separations between two points form the legs of a right triangle, and the distance is the hypotenuse: d = √((x₂−x₁)² + (y₂−y₁)²). The 3D version extends naturally by adding the z-component: d = √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²).

The midpoint formula finds the center point between two points. In 2D it is ((x₁+x₂)/2, (y₁+y₂)/2), and in 3D it adds ((z₁+z₂)/2). The slope of a line through two points, m = (y₂−y₁)/(x₂−x₁), describes how steep the line is. A slope of 0 means horizontal; undefined slope (division by zero) means vertical.

Distance calculations are fundamental in coordinate geometry, physics (displacement), GPS systems, computer graphics (rendering and collision detection), and data science (nearest-neighbor algorithms like k-NN). The Euclidean distance formula used here is the most common metric, though other distance metrics like Manhattan distance are used in specialized contexts.