An equation of state has been developed from the rotational partition function to describe the polymer molecule as a chain of rotators. The equation of state expresses the repulsion of the rotational modes of motion balanced by the attraction of the molecular segments as the molecular processes that determine the thermodynamic behavior of polymer melts. The equation of state accurately describes, generally within 0.1% of the specific volume, the pressure-volume-temperature behavior for polymer melts for which extensive data are available over a substantial temperature range at pressures up to 200 MPa. Four equation of state parameters are required to characterize a polymer, and the parameter values are reported for 26 polymers. Correlations are developed for the parameters with the molecular structure of the repeating segment of the polymer molecule. Using the correlations, the equation of state makes possible the estimation of volumetric and thermodynamic properties of polymers from knowledge of their chemical structure.