This paper describes formulation of a hand method which can be used to estimate the computed fundamental periods of vibration of steel eccentrically braced frames (EBFs). The developed method uses the Rayleigh's method as a basis and utilizes the roof drift ratio under seismic forces as a parameter. The roof drift ratio was obtained from EBF designs by considering different seismic hazard, number of stories, braced bay width, and link length to bay width ratio. A simple expression was developed to represent roof drift ratio as a function of the seismic hazard and bay width. The method was verified using design data produced as a part of this work and data published in literature. The verifications indicate that the proposed formulation is capable of providing acceptable estimates of the computed period. When compared with existing empirical period-height relationships the proposed formulation offers closer estimates with reduced scatter. The method was further refined to derive a new period height relationship. The accuracy of this relationship was verified using measured periods of EBF buildings.