In the past, experimentally observed dislocations were often interpreted using an isolated dislocation assumption because the effect of background dislocation density was difficult to evaluate. Contrarily, dislocations caused by atomistic simulations under periodic boundary conditions can be better interpreted because linear elastic theory has been developed to address the effect of periodic dislocation array in the literature. However, this elastic theory has been developed only for perfect dislocations, but not for dissociated dislocations. The periodic boundary conditions may significantly change the dissociation energy of dislocations and stacking fault width, which in turn, change the deformation phenomena observed in simulations. To enable materials scientists to understand the dislocation behavior under the periodic boundary conditions, we use isotropic elastic theory to analyze the thermodynamics of dissociated periodic dislocations with an arbitrary dislocation character angle. Analytical expressions for force, stacking fault width, and energies are presented in the study. Results obtained from the periodic dislocation array were compared with those obtained from isolated dislocations to shed light on the interpretation of experimentally observed and simulated dislocations.