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3D Unit Vector — result sheet
Normalize a nonzero three-dimensional Cartesian vector to a vector of Euclidean length one.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: u = v/|v| = (x/sqrt(x^2+y^2+z^2), y/sqrt(x^2+y^2+z^2), z/sqrt(x^2+y^2+z^2)).
A unit vector keeps the direction of a nonzero input while dividing every component by its Euclidean magnitude. The zero vector is rejected because it has no direction to normalize.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Vector x — The x component of the vector.; minimum -1000000; maximum 1000000
- Vector y — The y component of the vector.; minimum -1000000; maximum 1000000
- Vector z — The z component of the vector.; minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Vector x | 3 |
| Vector y | 4 |
| Vector z | 0 |
The unit vector is (0.6, 0.8, 0).
Assumptions and limits
- The input is a nonzero Cartesian 3D vector and the Euclidean L2 norm is the intended length.
- Components are treated as a direction-bearing triple; unit conversion, uncertainty, and downstream physical meaning are outside the calculation.
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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