Distance Formula Calculator
Find the distance between two points on the coordinate plane.
Straight-line distance between the two points.
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Formula
Examples
| Input | Result |
|---|---|
| (1, 2) and (4, 6) | d = 5 |
About this calculator
The distance formula gives the straight-line (Euclidean) distance between two points (x₁, y₁) and (x₂, y₂) in the plane. It is a direct application of the Pythagorean theorem: the horizontal gap (x₂ − x₁) and vertical gap (y₂ − y₁) form the legs of a right triangle, and the distance is the hypotenuse.
Because each difference is squared, the order of the points does not matter — swapping them gives the same result. The formula is widely used in geometry, physics, navigation, and computer graphics whenever you need the shortest distance between two locations.
Frequently asked questions
It comes from the Pythagorean theorem. The differences in x and y are the legs of a right triangle, so the distance (hypotenuse) is the square root of the sum of their squares.
No. Each difference is squared, so (x₂ − x₁)² equals (x₁ − x₂)². You get the same distance regardless of which point you call first.
Yes. The formula works for any real coordinates, positive or negative, because the squaring removes any sign before the square root.
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