The paper presents a new estimator, the multistate Bennett acceptance ratio (MBAR) estimator, for computing free energy differences and thermodynamic expectations from samples obtained from multiple equilibrium states. The MBAR estimator is an extension of the Bennett acceptance ratio (BAR) method and is designed to address the limitations of multiple histogram reweighting methods, such as bias due to energy binning and computational complexity. The MBAR estimator does not require discretization of the energy range, eliminating bias and reducing computational complexity. It provides a direct estimate of statistical uncertainties, which is crucial for comparing experimental and theoretical results. The estimator is asymptotically unbiased and has the lowest variance among known estimators for multiple equilibrium states. The paper illustrates the method by estimating the potential of mean force for a DNA hairpin system using data from multiple optical tweezer measurements under different external biasing potentials. The MBAR estimator is also applicable to data from simulations and single-molecule experiments, making it a versatile tool for statistical physics, computational chemistry, and single-molecule experiments.The paper presents a new estimator, the multistate Bennett acceptance ratio (MBAR) estimator, for computing free energy differences and thermodynamic expectations from samples obtained from multiple equilibrium states. The MBAR estimator is an extension of the Bennett acceptance ratio (BAR) method and is designed to address the limitations of multiple histogram reweighting methods, such as bias due to energy binning and computational complexity. The MBAR estimator does not require discretization of the energy range, eliminating bias and reducing computational complexity. It provides a direct estimate of statistical uncertainties, which is crucial for comparing experimental and theoretical results. The estimator is asymptotically unbiased and has the lowest variance among known estimators for multiple equilibrium states. The paper illustrates the method by estimating the potential of mean force for a DNA hairpin system using data from multiple optical tweezer measurements under different external biasing potentials. The MBAR estimator is also applicable to data from simulations and single-molecule experiments, making it a versatile tool for statistical physics, computational chemistry, and single-molecule experiments.