Parallelepiped Calculation

This function calculates various parameters of a parallelepiped. A parallelepiped is a three-dimensional figure formed by six parallelograms, 2 of which are opposite each other and are in parallel planes.

To perform the calculation, enter the three side lengths and the three angles. Then click on the 'Calculate' button.

Parallelepiped berechnen  Input Delete Entries Side length a Side length b Side length c Angle α Angle β Angle γ Decimal places 0 1 2 3 4 6   Results Surface S Volume V Height h

Parallelepiped properties

A parallelepiped is a geometric solid bounded by six parallelograms. Any two opposing parallelograms are congruent (coincident) and lie in parallel planes. It has twelve edges (four of which are parallel and of equal length) and eight corners, in which these edges converge at a maximum of three different angles to each other. Cuboids and rhombohedrons are special cases of the parallelepiped. The cube combines both special cases in one figure. The parallelepiped is a special prism with a parallelogram as a base.

Parallelepiped formulas

Volume (\(\small{V}\))

\(\displaystyle V=a\cdot b\cdot c\cdot {\sqrt {1+2\cdot \cos(\alpha )\cdot \cos(\beta )\cdot \cos(\gamma )-\cos ^{2}(\alpha )-\cos ^{2}(\beta )-\cos ^{2}(\gamma )}}\)

Surface (\(\small{S}\))

\(\displaystyle S=2\cdot a\cdot b\cdot \sin(\gamma )+2\cdot a\cdot c\cdot \sin(\beta )+2\cdot b\cdot c\cdot \sin(\alpha )\)

Height (\(\small{h}\))

\(\displaystyle h={\frac {a}{\sin(\alpha )}}\cdot {\sqrt {1+2\cdot \cos(\alpha )\cdot \cos(\beta )\cdot \cos(\gamma )-\cos ^{2}(\alpha )-\cos ^{2}(\beta )-\cos ^{2}(\gamma )}}\)