Distance Between Points Calculator
Calculate the straight-line distance between any two points on a coordinate plane. Based on the Pythagorean theorem, this calculator provides the distance, its square, and a step-by-step breakdown.
The distance formula calculates the straight-line (Euclidean) distance between two points in a coordinate plane. It is a direct application of the Pythagorean theorem.
The Distance Formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
The horizontal difference (delta x) and vertical difference (delta y) form the legs of a right triangle, and the distance is the hypotenuse.
Example:
The distance between (1, 2) and (4, 6) is sqrt((4-1)^2 + (6-2)^2) = sqrt(9 + 16) = sqrt(25) = 5.
Extensions:
In 3D: d = sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2). The Manhattan distance (city block distance) is |x2-x1| + |y2-y1|, useful for grid-based paths. The distance formula is foundational in physics, navigation, computer graphics, and machine learning (nearest-neighbor algorithms).