New closed-form mathematical expressions, in the time- and frequency-domain, are derived for estimating the arterial windkessel compliance. The proposed expressions assume the three-element windkessel to model the arterial system and require the measurements of the entire waveforms of arterial pressure and flow. The resistance parameters are estimated using the recently proposed energy-balance method, then compliance is analytically calculated in order to minimize the pressure error in the compliant element. The derived expressions remain valid even when the windkessel compliance is assumed to be pressure-dependent. Also, it is shown that the method, either time- or frequency-domain formulation, provides parameter estimates, which minimize the arterial pressure square error. The method has been applied to simulated data as well as to pressure and flow data measured in the ascending aorta of three anaesthetized dogs under different circulatory conditions.