The Madelung constants for binary ionic nanoparticles are determined. The computational method described here sums the Coulombic interactions of each ion in the particle without the use of partial charges commonly used for bulk materials. The results show size-dependent lattice energies. This is a useful concept in teaching how properties such as melting point are critically dependent on the size of the nanostructure. To use this method to determine the bulk Madelung constant, the summation must use a carefully constructed building unit. These are developed for NaCl, CsCl, and ZnS (zinc blende) structure types. (Contains 5 figures and 1 table.)