  This paper proposes a new volume function for calculation of the entropy of
planar granular assemblies. This function is extracted from the antisymmetric
part of a new geometric tensor and is rigorously additive when summed over
grains. It leads to the identification of a conveniently small phase space. The
utility of the volume function is demonstrated on several case studies, for
which we calculate explicitly the mean volume and the volume fluctuations.
