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3D Euclidean Distance — result sheet
Calculate the straight-line Euclidean 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: d = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2).
Subtract corresponding coordinates, square the three differences, add them, and take the nonnegative square root. The result is the straight-line distance in the same coordinate units as the inputs.
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 |
Differences are (3, 4, 12), so the Euclidean distance is sqrt(9 + 16 + 144) = 13 coordinate units.
Assumptions and limits
- Both points use the same Cartesian axes, origin, scale, and coordinate units.
- The distance is Euclidean straight-line distance through the coordinate space, not a constrained path or surface distance.
- 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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