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Volume of a Parallelepiped — result sheet
Calculate the volume of a parallelepiped from three edge vectors.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Volume = absolute value of A dot (B cross C).
The scalar triple product gives the oriented volume of three edge vectors. Taking the absolute value reports the physical volume regardless of vector order or orientation.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Vector A x — minimum -1000000; maximum 1000000
- Vector A y — minimum -1000000; maximum 1000000
- Vector A z — minimum -1000000; maximum 1000000
- Vector B x — minimum -1000000; maximum 1000000
- Vector B y — minimum -1000000; maximum 1000000
- Vector B z — minimum -1000000; maximum 1000000
- Vector C x — minimum -1000000; maximum 1000000
- Vector C y — minimum -1000000; maximum 1000000
- Vector C z — minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Vector A x | 2 |
| Vector A y | 0 |
| Vector A z | 0 |
| Vector B x | 0 |
| Vector B y | 3 |
| Vector B z | 0 |
| Vector C x | 0 |
| Vector C y | 0 |
| Vector C z | 4 |
Parallelepiped volume is 24 cubic units.
Assumptions and limits
- The three vectors share one Cartesian coordinate system and unit.
- The edge vectors start from one common vertex.
- Degenerate coplanar vectors correctly produce zero volume.
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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