To quickly and accurately solve the path length corresponding with the oxygen absorptivity of oxygen absorption passive ranging technology,this paper explores the mathematical model on oxygen absorptivity and path length.Firstly,the strong correlation of different absorption coefficient distributions under different temperatures and pressures was verified and the relation between absorption coefficient distributions and temperatures,pressures was given.Then,the mathematical model on oxygen absorptivity and path length was established by using Correlation-K Distribution(CKD) method and surface Earths model.Finally,the theoretical analysis and experimental checking were performed.The results show that this mathematical model not only well adapts to altered atmospheric models,but also quickly and accurately calculates the oxygen absorptivity curves of specified path and the target distances.The relative ranging error is 4.4% under average math mode,but the relative error is only 1% after eliminating background and reducing measurement errors.The conclusion shows that the math mode solves the ranging inverse problem of the oxygen absorption passive ranging technology,and provides some theoretical supports for the further optimiz and application of passive ranging technology.