Polynomial Path for the Calculation of Liquid State Free Energies from Computer Simulations, Tested on Liquid Water Abstract: The polynomial path is introduced for the calculation of liquid state free energies. The well characterized SPC, TIP4P and MCY water models were used to demonstrate its efficiency as well as its range of applicability in conjunction with Monte Carlo computer simulations using thermodynamic integration based on Gaussian quadratures. The technique employed is compared with the slow growth method (an other variant of thermodynamic integration), with the perturbation method and with the use of the grand-canonical ensemble.