In cellular networks, all base stations (BSs) do not continuously transmit i.e., the BSs transmit only when their queues are non-empty. This implies that the system resources are only partially loaded, and the dynamics of such a network differs significantly from that of a fully-loaded system. The coverage probability in a fully- and partially-loaded cellular network is analysed. We consider a regular spatial arrangement of base stations, and obtain the coverage probability in the presence of interference. More specifically, expressions for coverage probability are obtained for square and hexagonal lattices with full and partial loading. The coverage probability is obtained using properties of lattice sums which were first used in physics to analyse potentials in crystal structures. © 2013 IEEE.