Distance Between Two Points
The straight-line distance between two points on a plane.
Result
Distance
5.0000
How it works
The distance between two points in a plane is the Pythagorean theorem in disguise: d = √((x₂−x₁)² + (y₂−y₁)²). Draw the horizontal and vertical gaps between the points and you have a right triangle whose hypotenuse is the distance you want. From (1,2) to (4,6), the gaps are 3 and 4, so the distance is √(9+16) = 5 — the classic 3-4-5 triangle. Squaring the differences also removes any sign problem: the order of the two points never changes the result. The formula extends naturally to three dimensions by adding a term: d = √(Δx² + Δy² + Δz²). It underpins computer graphics, collision detection in games, nearest-neighbour searches and clustering algorithms — anywhere a machine needs to know "how far apart?".
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Frequently asked questions
Where does the formula come from?
From Pythagoras — the distance is the hypotenuse of a right triangle formed by the x and y differences.
Does it work in 3D?
The same idea extends to 3D by adding a (z₂−z₁)² term; this tool covers the 2D case.
Does the order of the points matter?
No. The differences are squared, so a negative gap gives the same result as a positive one — the distance from A to B always equals the distance from B to A.
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