We develop a rigorous error analysis for coarse-graining of defect-formation free energy. For
a one-dimensional constrained atomistic system, we establish the thermodynamic limit of the defectformation free energy and obtain explicitly the rate of convergence. We then construct a sequence of
coarse-grained energies with the same rate but significantly reduced computational cost. We illustrate
our analytical results through explicit computations for the case of harmonic potentials and through
numerical simulations.