It is useful to estimate peak floor accelerations consistent with the specified seismic hazard for ensuring the safety of rigid nonstructural components in structural systems. A modal combination rule is formulated here to estimate peak floor accelerations in a multistoried building directly in terms of the dynamic properties of the building and pseudo spectral acceleration ordinates of the base excitation. The formulation is developed under the framework of stationary random vibration theory for a linear, lumped-mass, classically damped, multi-degree-of-freedom system with the help of some approximations. A numerical study shows that the proposed rule performs well with the maximum average absolute error in any combination of building and excitation being less than 20% in case of 5% damping. Two simpler SRSS-type variants of the proposed rule, one considering modal cross-correlation and another ignoring this, are also shown to perform reasonably well, particularly when the building is not flexible to the ground motion.