In this work, we describe how to efficiently and reliably calculate p-x and T-x diagrams for binary mixtures of fluids. The method is based on the use of the Helmholtz energy density as the fundamental thermodynamic potential. Through the use of temperature and molar concentrations of the components as the independent variables, differential relationships can be constructed along the phase envelope surface, and this system of differential equations is then integrated to construct isotherms and isobars cutting through the phase envelope. The use of the Helmholtz energy density as the fundamental potential allows several models to be considered in this formalism, including cubic equations of state (Peng-Robinson, GC-VTPR, etc.) as well as high-accuracy multifluid equations of state (the so-called GERG mixture model). Examples of each class are presented, demonstrating the flexibility of this method. Source code, examples, and comprehensive analytic derivatives are provided in the Supporting Information. (c) 2018 American Institute of Chemical Engineers AIChE J, 64: 2745-2757, 2018