Distance Between Two Points (2D + 3D)

d = √(Δx² + Δy² [+ Δz²]). Pythagorean distance in the plane or 3-space.

Inputs

Result

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How to use this calculator

  • Enter two points' coordinates.
  • Read distance.

About this calculator

The distance formula is the Pythagorean theorem applied to the legs Δx and Δy: d = √(Δx² + Δy²). Foundational for coordinate geometry, GPS, computer graphics, machine learning (Euclidean distance). Manhattan distance |Δx| + |Δy| is an alternative — what a taxi drives on a city grid. Generalizes to 3D: d = √(Δx² + Δy² + Δz²).

Frequently asked

Why is this distance?+
Pythagorean theorem on right triangle with legs Δx and Δy. The hypotenuse is the straight line between points.
Manhattan vs. Euclidean?+
Euclidean: straight line. Manhattan: sum of absolute differences (city blocks). Often used in algorithms.
3D version?+
d = √(Δx² + Δy² + Δz²). Generalizes naturally — and to any number of dimensions.
GPS distance?+
On Earth's surface use haversine formula (great-circle distance), not flat Euclidean — Earth curves matter at distances >1 km.
Negative distance?+
Always non-negative (square root of sum of squares). Manhattan is also non-negative (absolute values).

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