We present a new computational technique to quantify the solubility of planar molecules in a solvent. Solubility is calculated as the critical concentration at which solute molecules cease to stack as columns, but rather aggregate in all directions. An explicit expression for the solubility is obtained, which involves the potential of mean force between two solute molecules as a function of their center-of-mass distance in the limit of infinite dilution. This function can be easily obtained from molecular dynamics simulations involving a pair of solute molecules in a solvent using the umbrella-sampling method. As a validation of our approach, we use a generic coarse-grained molecular model to represent the molecular interactions of polycyclic-aromatic-hydrocarbon. Within that coarse-grained model, the solubility of pyrene and acenaphthene in heptane is estimated through large molecular dynamics simulations and compared to the experimental results. The umbrella-sampling method, applied to single pairs of these molecules in the solvent, provides the values of the critical cluster size in the theoretical model of molecular stacking. Umbrella-sampling simulations for the first members of the polycyclic-aromatic-hydrocarbon series then are used to predict their solubilities through our theoretical method. Within the typical uncertainty associated with theoretical solubility estimates, the agreement of our results with the experimental values is quite remarkable for most of the members of the series in a wide range of molecular masses, which confirms the general validity of the method in the case of planar molecules. Among the molecules explored, agreement with experiment fails for anthracene, for which the experimental solubility is clearly out of the general trend along the polycyclic-aromatic-hydrocarbon series, indicating that the coarse-grained representation used here is not able to capture its peculiarity. The new methodology can be applied to planar molecules to obtain relatively accurate values of solubility at a very low computational cost.