📏 Distance Formula Calculator
Enter two coordinate points and this calculator uses the distance formula to find the straight-line distance between them.
What This Calculator Does
The Distance Formula Calculator finds the straight-line (Euclidean) distance between two points plotted on a standard x-y coordinate plane. It is a core tool in algebra, geometry, and trigonometry, and it also shows up in everyday problems like measuring the shortest path between two locations on a map grid.
The Formula
The distance formula comes directly from the Pythagorean theorem. For two points (x1, y1) and (x2, y2), the distance d is: d = sqrt[(x2 – x1)^2 + (y2 – y1)^2]. The horizontal difference and vertical difference form the two legs of a right triangle, and the distance itself is the hypotenuse.
Reading the Results
Besides the final distance, the calculator also shows the horizontal difference (dx), vertical difference (dy), the squared distance (useful as an intermediate step in geometry proofs), and the midpoint of the segment connecting the two points, which is handy when a problem asks for both the distance and the center of a line segment.
- Works with positive, negative, or zero coordinates
- Same formula applies whether the points represent map coordinates, graph points, or pixel positions
- For general educational and planning use