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

Formulas for the Parallelepiped

Volume

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

Surface

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

Height

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