The importance of Electric Energy Storage (EES) for the transformation to an energy grid with a large share of Renewable Energy Source (RES) has been studied and shown for many decades. While larger storage systems might provide more energetic benefits for the overall grid, they also require higher investment and capital costs. Hence the question of the cost-optimal size of EES and RES is commonly stated in public debates and the related literature. This minimization problem is mainly solved by combining simulation and optimization methods. Even though this enables the analysis of highly complex scenarios, the configuration and computation time are high, and many of the found methods are not reproducible. Within our paper, we introduce an analytical solution for calculating the cost-optimal capacity of an EES that is derived from results computed by the Effective Energy Shift (EfES) algorithm.