This paper describes formulation of a hand method that can be used to estimate the computed fundamental periods of vibration of building structures in general and steel eccentrically braced frames (EBFs) in particular. The developed method uses the Rayleigh's method as a basis and utilizes the roof drift ratio (RDR) under seismic forces as a parameter. To obtain RDR, more than 4000 EBFs were designed by considering the seismic hazard, number of stories, braced bay width and link length to bay width ratio as prime variables. A model was developed to estimate RDR, which depends on the rigid plastic deformation mechanism for a typical EBF. The method was verified using design data produced as a part of this work as well as 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 new period-height relationships for two different seismicity regions. The accuracy of the relationship for high seismic regions was verified using measured periods of EBF buildings. Copyright (c) 2014 John Wiley & Sons, Ltd.