This paper introduces a novel detailed formulation for analytically determining the maximum power point (MPP) of a photovoltaic (PV) module. The approach involves an analytical approximation of a 4-parameter PV model, taking into account the series resistance, which serves as the initial value for the fixed-point method to enhance accuracy. Additionally, the paper includes a statistical analysis of convergence to highlight the method’s limitations. The performance of the proposed method is evaluated against actual measurements of over one hundred thousand current-voltage (I-V) characteristic curves from eight different PV modules, as reported by the National Renewable Energy Laboratory (NREL), and is also compared with two existing literature approximations. Furthermore, a sensitivity analysis of the solution error under varying irradiance and temperature conditions is conducted. The method demonstrates high accuracy for engineering applications.