Sizing of widely deployed ultracapacitor stack is an essential requirement in design of energy storage systems. Unlike a linear capacitor that displays constant capacitance, UCs exhibit considerable nonlinearity in the form of voltage-dependent capacitance and notable variation in characteristics during operation. Analyzing the behavior of overall UC bank that consists of several stacked nonlinear UC cells and evaluating its effective capacitance is therefore critical. In this paper, an exact-analysis framework is presented for characterizing the nonlinear behavior of the overall UC stack. Closed-form expressions for stacks effective capacitance, terminal voltage characteristics, and stored energy are derived as a function of unit cell nonlinear parameters and number of cells, using which deviations in stack behavior from linear characteristics are analytically captured. It is shown that the resultant stack of existing method will either be over-sized and expensive, or insufficient to meet ESS specifications in practice. To address these limitations, an improved stack design method is proposed based on the nonlinear UC model, which optimizes the size of UC stack and guarantees that the ESS specifications are accurately met. Experimental results on two UC stack hardware prototypes validate the accuracy of proposed nonlinear analysis and the improved design method for ride-through applications.