The capacitance of an N-electron system is established by deriving the atomistic connection between the capacitive energy, the ionization potential, and the electron affinity of the charged system; it is shown further that this connection leads to the linkage of the capacitive energy to the difference between the lowest unoccupied and the highest occupied Kohn-Sham orbital energies of the system. An illustrative example is used to show explicitly the microscopic behavior of the derived capacitance for a finite electron system, and to discuss the tendency of the derived capacitance to limit toward the classical electrostatic capacitance as the system becomes macroscopically large. Discussions relevant to atomic and molecular systems are included.