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3D Manhattan Distance — result sheet
Calculate the axis-aligned Manhattan distance between two ordered points in a three-dimensional Cartesian coordinate system.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: d1 = |x2 - x1| + |y2 - y1| + |z2 - z1|.
Take the absolute difference along each Cartesian axis and add the three nonnegative contributions. The result represents travel restricted to axis-aligned segments in the entered coordinate units.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Point 1 x — coordinate units; The x-coordinate of the first Cartesian point.; minimum -1000000; maximum 1000000
- Point 1 y — coordinate units; The y-coordinate of the first Cartesian point.; minimum -1000000; maximum 1000000
- Point 1 z — coordinate units; The z-coordinate of the first Cartesian point.; minimum -1000000; maximum 1000000
- Point 2 x — coordinate units; The x-coordinate of the second Cartesian point.; minimum -1000000; maximum 1000000
- Point 2 y — coordinate units; The y-coordinate of the second Cartesian point.; minimum -1000000; maximum 1000000
- Point 2 z — coordinate units; The z-coordinate of the second Cartesian point.; minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Point 1 x | 1 |
| Point 1 y | 2 |
| Point 1 z | 3 |
| Point 2 x | 4 |
| Point 2 y | 6 |
| Point 2 z | 15 |
Absolute differences are (3, 4, 12), so the Manhattan distance is 3 + 4 + 12 = 19 coordinate units.
Assumptions and limits
- Both points use the same Cartesian axes, origin, scale, and coordinate units.
- Movement is modeled as axis-aligned travel, so diagonal shortcuts are not included.
- Coordinates are finite real numbers within the displayed software bounds.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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