Free · Mathematics models
Parallelepiped Volume and Surface Area
Compute geometry from three edge vectors, four vertices or edge lengths with included angles.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
Perpendicular edge vectors of lengths 2, 3 and 4 meters give volume 24 cubic meters and surface area 52 square meters.
Volume is the absolute scalar triple product; surface area is twice the sum of the three cross-product magnitudes.
Worked example
Enter these known values and leave the other values blank.
- a₁
- 2 m
- a₂
- 0 m
- a₃
- 0 m
- b₁
- 0 m
- b₂
- 3 m
- b₃
- 0 m
- c₁
- 0 m
- c₂
- 0 m
- c₃
- 4 m
- Surface area of the parallelepiped
- 52 m²
- Volume of the parallelepiped
- 24 m³
Assumptions and limitations
- All three captured entry modes describe adjacent edges from one common vertex. The sign of the scalar triple product denotes orientation; volume uses its magnitude.
- Angle mode requires a physically realizable Gram matrix. Coplanar edges produce zero volume; collinear edges can also give zero surface area.
- This describes a straight-edged parallelepiped, not an arbitrary hexahedron.
- Clear the unknown numerical field before using a supported inverse; selection controls retain their captured branches.
Common questions
What assumptions matter for this model?
All three captured entry modes describe adjacent edges from one common vertex. The sign of the scalar triple product denotes orientation; volume uses its magnitude.
What does this model leave out?
This describes a straight-edged parallelepiped, not an arbitrary hexahedron.
References
Authored accessible explanations preserve each captured diagram mode and its geometric relationships.