We introduce the theoretical background needed to perform thermodynamic calculations using reverse Monte Carlo (RMC). The theory is developed for binary A_{x}B_{1-x} lattice systems. The main assumption is that the arrangement of A and B atoms can be described using short-ranged order (SRO) parameters. The detailed balance equation, which is expressed in terms of SRO parameters, is solved to obtain the equilibrium SRO parameter value for the given material interactions, temperature, and composition. Thermodynamic properties, such as the chemical potential, are evaluated using the equilibrium SRO parameter value. RMC enables the calculation of the probability distribution of the local atomic environments, which is needed in the detailed balance equation. We illustrate the application of our method to bulk lattice materials with different first nearest neighbor pair interactions. The main advantage of our approach is that the probability distribution from RMC can be stored in form of look-up tables, and used with a variety of interaction strengths and temperature for rapid estimation of thermodynamic properties. In all examples, the chemical potential is accurately evaluated in the matter of a few seconds on a desktop computer.