Distance Formula Calculator
Enter coordinates for two points to get the straight-line distance, with a live graph in 2D, midpoint, slope, angle, and clear working you can check by hand.
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Result
Drag point A or B to move it. The inputs update to match.
Interactive graph is available in 2D mode. 3D results still show the full numeric breakdown below.
The formula
In 2D, d = √((x₂−x₁)² + (y₂−y₁)²). In 3D, add (z₂−z₁)² under the root. That is the Pythagorean theorem on the coordinate differences.
Worked example
- Points A(0, 0) and B(3, 4).
- Δx = 3 − 0 = 3, Δy = 4 − 0 = 4.
- d = √(3² + 4²) = √25 = 5.
Result: Distance = 5
How the distance formula works
The straight-line length between two points is the hypotenuse of a right triangle whose legs are the gaps along each axis.
Link to the Pythagorean theorem
Treat Δx and Δy (and Δz in 3D) as the legs of a right triangle. The hypotenuse d is the Euclidean distance.
Signs and point order
Squaring the differences removes sign, so swapping A and B yields the same distance. Negative coordinates and decimals work without special handling.
Units
The result uses the same unit as your axes. Optional unit labels are for display only — they do not convert values.
What this does not model
Great-circle (Earth surface) distance and GPS route length need geodetic formulas, not a flat Euclidean tool.
Interesting facts
Straight-line distance
This gives the shortest distance “as the crow flies” between two points in flat space.
Pythagorean link
The formula comes directly from the Pythagorean theorem, using axis gaps as triangle legs.
Works with negatives and decimals
Coordinates can be positive, negative, or decimal values.
Frequently asked questions
Yes. Negative x, y, or z values work normally.
No. Swapping point A and B gives the same distance.
The distance is 0.
No. Switch to 3D (x, y, z) to include a z difference under the square root.
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.