Due to their thin-walled characteristics, axially loaded circular cylindrical shells (CCSs) commonly undergo buckling failure. The limiting buckling stress of such shells has not yet been fully developed due to a wide range of influencing parameters such as sensitivity to imperfections, nonlinearity, and buckling mode. It has been proved early, and in this study, that the nonaxisymmetric buckling stress can be one of the remedies that casts into eliminating the overestimation caused by the classical axisymmetric buckling formula. However, the complex nonlinear constrained optimization required to obtain the nonaxisymmetric buckling stress and mode remains to be the main obstacle for practicing engineers to approach the nonaxisymmetric buckling. In this study, the nonaxisymmetric buckling formula has been cast in a compact form and possible approaches to utilize it have been discussed considering the degree of user knowledge and availability of computational tools. Moreover, it has been used to derive a closed-form buckling stress formula that considers the effect of all geometric and material properties. The proposed closed-form formula predicts buckling stress that is always less than that of the classical formula for L/R greater than 0.91 and the amount of reduction increases with the increase of L/R ratio. In comparison with the exact nonaxisymmetric buckling formula, the proposed closed-form formula yields buckling stress within 4%. Thus, it shares the simplicity of the classical axisymmetric buckling formula and the accuracy of the nonaxisymmetric buckling formula.