Classical free-energy methods depend on the definition of physical or nonphysical integration paths to calculate free-energy differences between states. This procedure can be problematic and computationally expensive when the states of interest do not overlap and are far apart in phase space. Here we introduce a novel method to calculate free-energy differences that is path-independent by transforming each end state into a reference state in which the vibrational entropy is the sole component of the total entropy, thus allowing direct computation of the relative free energy. We apply the method to calculate side-chain entropies of a beta-hairpin-forming peptide in a variety of backbone conformations, demonstrating its importance in determining structural propensities. We find that low-free-energy conformations achieve their stability through optimal trade off between enthalpic gains due to favorable interatomic interactions and entropic losses incurred by the same.