The input energy to a base-isolated (BI) building during an earthquake is considered and formulated in the frequency domain. The frequency-domain approach for input energy computation has some notable advantages over the conventional time-domain approach. Sensitivities of the input energy to the BI building are derived with respect to uncertain parameters in the base-isolation system. It is demonstrated that the input energy can be of a compact form via the frequency integration of the product between the input component (Fourier amplitude spectrum of acceleration) and the structural model component (so-called energy transfer function). With the help of this compact form, it is shown that the formulation of earthquake input energy in the frequency domain is essential for deriving the sensitivities of the input energy to the BI building with respect to uncertain parameters. The sensitivity expressions provide us with information on the most unfavorable combination of the uncertain parameters which leads to the maximum energy input.