Volume of a Parallelepiped Calculator

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Choose how you know your parallelepiped: by its spanning vectors, its edge lengths and included angles, or by four corner points.
x-component of the first edge vector a.
Volume
24

Volume of the parallelepiped (cubic units)

Surface area52
Base face area (|a x b|)6
Perpendicular height4
Scalar triple product24
Volume (cubic units)24
Surface area (sq units)52
Base face area (sq units)6

The parallelepiped has a volume of 24.0000 cubic units.

  • The total surface area across all six parallelogram faces is 52.0000 square units.
  • The base face (spanned by vectors a and b) has area 6.0000 square units.
  • The perpendicular height from the base to the opposite face is 4.0000 units, so Volume = Base area x Height = 6.0000 x 4.0000 = 24.0000.
  • The scalar triple product is 24.0000: the vectors form a right-handed system.

Next stepTo scale the shape, multiply all edge lengths by a factor k - the volume scales by k^3 and the surface area scales by k^2.

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