2D Distance Calculator

This calculator takes two ordered pairs, (x1, y1) and (x2, y2), and returns the straight-line distance between them in a two-dimensional coordinate system. It applies the distance formula, which measures direct separation rather than grid walking.

Coordinate entry matters because the formula depends on differences: the horizontal change is x2 − x1 and the vertical change is y2 − y1. Swapping the points does not change the final distance because squaring removes sign, but mixing x with y or typing one coordinate in the wrong place changes the result.

The distance formula comes from the Pythagorean theorem: the differences in x and y form the legs of a right triangle, and the distance is the hypotenuse.

The formula section below provides the expression and a compact meaning of each variable so you can implement the same calculation in a worksheet, a program, or manually.

This section explains the manual workflow for computing distance from coordinates without using a tool. The process reduces the geometry to two coordinate differences, squares them to avoid sign issues, sums them to combine perpendicular components, and then applies a square root to return to the original unit scale.

The step list below is structured so each intermediate value can be checked. Worked example: take (x1, y1) = (−2, 5) and (x2, y2) = (7, 1). Δx = 7 − (−2) = 9; Δy = 1 − 5 = −4. Squares: 81 and 16. Sum S = 97. Distance d = √97 ≈ 9.85 units.

Choose the distance method that matches what you are measuring. A 2D distance (Euclidean distance) is appropriate on a plane when you want the direct straight-line separation between two coordinate points.

Related computations often differ only in inputs or dimension: line-segment length uses the same idea when endpoints are known; coordinate distance is the same concept in analytic geometry; Euclidean distance generalizes beyond 2D by adding more squared coordinate differences.