Aimed at the puzzle that the maximum power point (MPP) parameters of photovoltaic (PV) cells cannot be readily solved, this paper starts with a detailed theoretical analysis on the analytical solutions for MPP parameters under the ideal circuit model on the grounds of the mean value theorem, and then the exact analytical expressions for MPP parameters are deduced by referring to the general circuit model of PV cells. Of the analytical expressions deduced in this paper, the variables are directly correlated, and their solutions are handy and demanding no iterative algorithms. Next, the effects of cell temperature and solar irradiance on each component of the analytical expressions are dissected in detail, with the minor components ignored, so as to uncover a linear relationship among MPP parameters, cell temperature and solar irradiance. Eventually, approximate linear estimation formulas for MPP parameters are obtained. The validity of the two deduced formulas is then verified by various simulation experiments and field measurement experiments, both of which prove that the acquired parameters have a high accuracy for practical applications. Moreover, the formulas are open for selection or further simplification in accordance with different requirements on computation loads of algorithms or varying needs for parameter accuracy.