In the selection of liquids and liquid mixtures to dissolve a given material, the two-dimensional solubility parameter is shown to be both easier to use and much more accurate than the commonly used three-dimensional solubility parameter. The solubility parameter of each liquid is represented as a vector with complexing and field force components. The complexing solubility parameter component characterizes the ability of a liquid to form interactions that require a specific orientation between molecules while the field force solubility parameter component includes dipole interactions, which usually are only significant for associated liquids, like alcohols, and dispersion interactions. On the basis of five postulates, the solvent power of each liquid is represented by a point in two-dimensional solubility parameter space while the set of solvents for a given material are represented by the area of a polygon. The assignment of solubility parameter components for 50 liquids were made on the basis of their ability or inability to dissolve 35 polymers and 3 dyes in this study and 33 polymers from a previous study and resulted in a 99.5% accuracy of the placement of nonsolvents outside and of solvents inside the solubility areas. These solubility areas enabled the correct prediction of over 100 solvents formed from mixtures of liquids that individually are nonsolvents. Finally, as an example, the two-dimensional solubility parameter was applied to the selection of solvents for forming colored, spherical polymer particles, encapsulated in clear polymer shells by spray drying.