Three regularities have been introduced for liquids (T < T-C and ρ > ρ(C)) based on average potential energy. The experimental data have been. and p for all isotherms of a liquid, where used to show the validity of the regularities. First, there exists near-linearity relation between PiVm4 P-i and ρ for all isotherms of a liquid, where P-i and ρ are internal pressure and density, respectively. Second, (2Z-1)V-m(3), changes linearly with p for each isotherm of any liquid, where Z and V-m are compressibility factor and molar volume, respectively. Third, a new regularity using the definition of bulk modulus and our new equation of state between reduced bulk modulus and density has been introduced, that is (B-t-0.5)V-m(3), versus ρ must be linear for all isotherms of a liquid where B-t is the reduced bulk modulus. A new equation of state has been also derived. The density of some liquids in the extensive ranges of temperature and pressure has been calculated using the new equation of state. The densities calculated from this equation agree with experiment to better than 0.3%. The new equation of state can predict internal pressure, thermal expansion coefficient, and isothermal compressibility of liquids within experimental error. © 2004 Elsevier B.V. All rights reserved.