Macrocycles have been emerging as a very important drug class in the past few decades largely due to their expanded chemical diversity benefiting from advances in synthetic methods. Macrocyclization has been recognized as an effective way to restrict the conformational space of acyclic small molecule inhibitors with the hope of improving potency, selectivity, and metabolic stability. Because of their relatively larger size as compared to typical small molecule drugs and the complexity of the structures, efficient sampling of the accessible macrocycle conformational space and accurate prediction of their binding affinities to their target protein receptors poses a great challenge of central importance in computational macrocycle drug design. In this article, we present a novel method for relative binding free energy calculations between macrocycles with different ring sizes and between the macrocycles and their corresponding acyclic counterparts. We have applied the method to seven pharmaceutically interesting data sets taken from recent drug discovery projects including 33 macrocyclic ligands covering a diverse chemical space. The predicted binding free energies are in good agreement with experimental data with an overall root-mean-square error (RMSE) of 0.94 kcal/mol. This is to our knowledge the first time where the free energy of the macrocyclization of linear molecules has been directly calculated with rigorous physics-based free energy calculation methods, and we anticipate the outstanding accuracy demonstrated here across a broad range of target classes may have significant implications for macrocycle drug discovery.