Why the distance formula is just Pythagoras
Picture the two points on a grid. The horizontal gap between them (Δx) and the vertical gap (Δy) form the two legs of a right triangle, and the straight line connecting the points is its hypotenuse.
The Pythagorean theorem says the hypotenuse squared equals the sum of the two legs squared. Taking the square root of that sum gives the distance, which is exactly what the formula computes.
Reading Δx and Δy
Alongside the distance, the calculator reports the signed differences Δx and Δy. A positive Δx means the second point is to the right of the first; a negative one means it is to the left. The same logic applies vertically for Δy.
These signed values are useful for finding direction, not just distance. They feed directly into slope (Δy ÷ Δx) and into the angle of the line.
Points to keep in mind
Swapping the two points never changes the distance — it only flips the signs of Δx and Δy — because squaring removes the sign. Distance is always zero or positive.
Both points must use the same coordinate system and the same unit. The formula extends naturally to three dimensions by adding a (z₂ − z₁)² term, but this tool works in the flat plane.
Formula
distance = √((x₂ − x₁)² + (y₂ − y₁)²)Frequently asked questions
- Does the order of the points matter?
- No. Distance is the same either way; only the signs of Δx and Δy flip.