This article presents the theoretical relationship between the site amplification ratio of the input energy spectrum for a single‐degree‐of‐freedom system (SDOF) and that of the Fourier amplitude spectrum (FAS). The relationship indicates that the input energy spectral ratio is the result of smoothing the square of the Fourier amplitude spectral ratio. The spectral window for smoothing is determined by the bedrock‐motion FAS and the oscillator transfer function for the relative velocity. The characteristics of the input energy spectral ratio were derived based on the idea of smoothing and confirmed based on real seismic records. The findings of this study contribute to a better understanding of site effects on the input energy spectrum.