By Zencalcy Editorial TeamLast reviewed About us
City-block distance: |x₂−x₁| + |y₂−y₁|. When movement is restricted to a grid — streets, warehouses, robot navigation — this is the true travel distance, not the straight line.
Grid distance |dx| + |dy| for navigation and robotics.
d = |x₂−x₁| + |y₂−y₁|
| Symbol | Meaning |
|---|---|
| d | Manhattan (L¹ / taxicab) distance |
(1,2)→(4,6): |3| + |4| = 7 — longer than the Euclidean 5, because diagonals are forbidden.
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Content updated: September 2026