Several solutions in the form of curve families, simplified closed form equations and numerical approaches have been proposed by researchers for evaluating the stability of individual web-tapered compression members, while frame instability is rarely addressed and accounted for. In this paper, using structural mechanics concepts and curve fitting, the lateral stiffness for a constrained web-tapered column is approximated in a simple parabolic form. Utilizing the simplified stiffness function and following the story sway concept, an elastic effective length factor (K-factor) formula is presented to be used for sway frames that are composed of web tapered columns. A proper length modification factor formula for partially tapered restraining girders is proposed to facilitate stiffness ratio calculations at the columns’ ends. Moreover, a closed form equation for individual column K-factor evaluation is introduced which can be considered as a sound alternative to the available approaches which function under the basis of curve families. The proposed method improves the K-factors resulted from a member instability (p-δ) study by considering the inter-story interaction of columns known as frame instability (P-Δ) effects. This method is capable of considering the contribution of any leaning column in the story stability assessment. Some examples are considered to illustrate the proposed method’s efficiency and verify its accuracy. Based on the studied frames and by comparing the results and solution procedure with available methods, it is shown that the proposed method removes difficulties of using curve families or solving eigenvalue problems by employing single valued closed form formulas. Also, the solution algorithm is not restricted to columns with ideal base fixities and it can deal with any restraining base condition with satisfactory accuracy. Furthermore, the effects of frame asymmetry and existence of any leaning column are simply accounted for by following the pr