The metric tensor  is sometimes used for calculations involving the unit cell and is defined (in matrix form) as:
In two dimensions,
In three dimensions,
The distance between two points  and  in the unit cell can be determined from the relation:
The distance from the origin of the unit cell to a point  within the unit cell can be determined from the relation:
The angle formed from three points ,  (apex), and  within the unit cell can determined from the relation:
The volume of the unit cell,  can be determined from the relation: