The resistance–capacitance (RC) model is one of the most applicable circuits for modeling the charging and discharging processes of supercapacitors (SCs). Although this circuit is usually used in the electric and thermal investigation of the performance of SCs, it does not include leakage currents. This paper presents exact analytical formulas of leakage-current-based supercapacitor models that can be used in industrial applications, i.e., constant-power-based applications. In the proposed model, current and voltage are represented as a solution of nonlinear equations that are solved using the standard Newton method. The proposed expressions’ accuracy is compared with the results obtained using traditional numerical integration methods with leakage current formulation and other methods, found in the literature, with no leakage current formulation. The results confirm that including leakage current represents a more accurate and realistic manner of modeling SCs. The results show that the derived expressions are precise, allowing the generation of results that closely match those obtained using traditional numerical-based methods. The derived expressions can be used to investigate SCs further and achieve more accurate and efficient regulation and control of SCs in different applications.