Abstract: To accurately calculate the inflection point of gas adsorption in deep coal seams, this study employs partial derivative theory of multivariate functions to quantitatively analyze the effects of temperature and pressure on the adsorption capacity. It accurately defines the critical depth by using the concept of multivariate function extremum and constructs an objective function closely related to the burial depth. A solution method integrating global scanning and the Brent local optimization algorithm is proposed. This method introduces physical constraints to filter optimal solutions, resulting in a critical depth calculation method applicable to various adsorption models. Compared with conventional methodologies, this approach requires less experimental data and enhances computational efficiency. The strong correlation between the calculated results and the measured data confirms the reliability and accuracy of the proposed method.