Distance Formula Calculator
Enter coordinates for two points on a 2D plane to calculate straight-line distance.
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Result
The formula
Use the Euclidean distance formula for two points (x1, y1) and (x2, y2).
Worked example
- Points A(0, 0) and B(3, 4)
- Δx = 3 − 0 = 3, Δy = 4 − 0 = 4
- d = √(3^2 + 4^2) = √25 = 5
Result: Distance = 5
How the distance formula works
The straight-line length between two points on a flat plane is the hypotenuse of a right triangle whose legs are the horizontal and vertical gaps.
Link to the Pythagorean theorem
Treat Δx and Δy as the legs of a right triangle. The hypotenuse d is √(Δx² + Δy²). The distance formula is that relationship written for coordinates.
Signs and point order
Squaring the differences removes sign, so swapping point A and point B yields the same distance. Negative coordinates and decimals work without special handling.
Units
The result uses the same unit as your axes. If x and y are in meters, d is in meters. Mixing feet on one axis and meters on the other is invalid.
What this does not model
3D distance and great-circle (Earth surface) distance are out of scope. Map or GPS route length needs geodetic formulas, not a flat-plane Euclidean tool.
Interesting facts
Straight-line distance
This gives the shortest distance "as the crow flies" between two points on a flat coordinate plane.
Pythagorean link
The formula comes directly from the Pythagorean theorem, using Δx and Δy as triangle legs.
Works with negatives and decimals
Coordinates can be positive, negative, or decimal values.
Frequently asked questions
Yes. Negative x or y values work normally.
No. Swapping point A and B gives the same distance.
The distance is 0.
Yes, this version calculates distance on a 2D plane.
Squaring removes sign direction and follows the right-triangle relation behind Euclidean distance.
References
- Distance formula in the plane Euclidean distance from the Pythagorean theorem.
- Pythagorean theorem Mathematical background for Δx/Δy distance calculations.