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Manhattan (Taxicab) Distance Between Two 3-D Points Calculator

d_M = |x₂ − x₁| + |y₂ − y₁| + |z₂ − z₁|.

Compute the L¹ (Manhattan / taxicab) distance between two points in 3-D space: d = Σ |coord₂ − coord₁|. The distance you'd traverse on a square grid moving only along axis-aligned directions. Frequently used in clustering, k-NN with categorical-style features, and image processing.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

d_M = |Δx| + |Δy| + |Δz|.

In depth

Compute the L¹ (Manhattan / taxicab) distance between two points in 3-D space: d = Σ |coord₂ − coord₁|. The distance you'd traverse on a square grid moving only along axis-aligned directions. Frequently used in clustering, k-NN with categorical-style features, and image processing.