The calculation of the volume as a function of the lattice parameters for all systems

The volume of the unit cell can be calculated from the lattice constant lengths and angles. If the unit cell sides are represented as vectors, then the volume is the dot product of one vector with the cross product of the other two vectors. The volume is represented by the letter V. For the general unit cell (triclinic system)

${\displaystyle V=abc{\sqrt {1+2\cos \alpha \cos \beta \cos \gamma -\cos ^{2}\alpha -\cos ^{2}\beta -\cos ^{2}\gamma }}.}$

Cubic system:

V = a^3


Tetragonal system:

V = a^2 . c

Orthorhombic system:

V = a.b.c

Hexagonal system:


V = a^2.c.sin 120


Monoclinic system: with α = 90°, γ = 90°




Rhombohedral system:

Make alpha=betha=gama in the général formula

Reference: https://en.wikipedia.org/wiki/Lattice_constant