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Distance Between Two Points (3D)

Distance between two points in 3D space

How it is calculated

The tool takes two points, (x1, y1, z1) and (x2, y2, z2), subtracts coordinates axis by axis and combines the differences: d = √(Δx² + Δy² + Δz²), with Δx = x2 − x1 and so on. The answer is in the same unit as your coordinates, and the tool never converts units. All six values are required; if any is missing nothing is shown. Negative and decimal coordinates are fine, and since each difference is squared the order of the two points does not matter. The result is rounded to two decimals.

Worked example

Point A is (1, 2, 3) and point B is (4, 6, 15). Differences: Δx = 4 − 1 = 3, Δy = 6 − 2 = 4, Δz = 15 − 3 = 12. Squares: 9 + 16 + 144 = 169. Square root: √169 = 13.00, in whatever unit the coordinates use.

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Common mistakes

  • Mixing units between axes, for example x and y in metres but z in centimetres.
  • Pairing coordinates incorrectly, such as entering x1 and x2 for the same point instead of the two x values of different points.
  • Leaving z at blank for a flat problem: all six fields are needed, so enter 0 for both z values in 2D.
  • Expecting a path length. The result is the straight line between the points, not the distance along a road, surface or curved route.
  • Using latitude and longitude as x and y; degrees are not lengths, so the result is meaningless on a globe.

About this calculator

This calculator extends the Euclidean distance formula to three dimensions: d = √((x2−x1)² + (y2−y1)² + (z2−z1)²), the natural generalization of the 2D Pythagorean formula obtained by applying it twice — once in a horizontal plane, then again with the vertical (z) difference.

3D modelers and game developers use it constantly for collision detection and camera-distance checks, engineers use it to compute clearances between components in CAD assemblies, and astronomers use the same formula (with much larger coordinates) to find the straight-line distance between stars given their positions in 3D space.

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