One of the most important design parameters of columns is their effective length in buckling. In the past, because of lack of analytical solution for differential equation of deformation of a tapered column, determination of its effective length was done by numerical methods which result in approximate solutions. In recent years, due to development of very powerful mathematical software’s, one can obtain analytical solution of equation of deformation and accurately find the coefficient of effective length. It will also facilitate to evaluate the values of errors of the past methods. The structure considered in this research is a one- bay gabled frame with tapered members that are solved for state of free to sway with hinged bases.In this research by equating the external work on the structure with its internal flexural strain energy of buckling, and imposing the boundary conditions and compatibility conditions, an equation is found from which the critical load of the structure and accordingly the coefficient of effective length of its columns is obtained. After analysis and obtain of precise graphs, that are more simple to use than graphs of AISC code of practice, the results are compared to the results of previous approximate methods.