When the two intersecting planes are described in terms of Cartesian coordinates by the two equations 
the dihedral angle,  between them is given by:
and satisfies  It can easily be observed that the angle is independent of  and .
Alternatively, if  and  are normal vector to the planes, one has
where  is the dot product of the vectors and  is the product of their lengths.
 and b and through b and b, respectively. -->
The absolute value is required in above formulas, as the planes are not changed when changing all coefficient signs in one equation, or replacing one normal vector by its opposite.
However the absolute values can be and should be avoided when considering the dihedral angle of two half planes whose boundaries are the same line. In this case, the half planes can be described by a point  of their intersection, and three vectors ,  and  such that ,  and  belong respectively to the intersection line, the first half plane, and the second half plane. The dihedral angle of these two half planes is defined by 
and satisfies  In this case, switching the two half-planes gives the same result, and so does replacing  with  In chemistry (see below), we define a dihedral angle such that replacing  with  changes the sign of the angle, which can be between  and .