Complex impedance data were collected for eight sandstones at various levels of water saturation (S w ) in the frequency range of 5 Hz to 4 MHz. The measurements were made using a two-electrode technique with platinum electrodes sputtered onto the flat faces of disk-shaped samples. Presentation of the data in the complex impedance plane shows clear separation of the response due to polarization at the sample-electrode interface from the bulk sample response. Electrode polarization effects were limited to frequencies of less than 60 kHz, allowing us to study the dielectric constant kappa ' of the sandstones in the frequency range of 60 kHz to 4 MHz. kappa ' of all samples at all levels of saturation shows a clear power-law dependence upon frequency. Comparing the data from the eight sandstones at S w = 0.36, the magnitude of the frequency dependence was found to be proportional to the surface area-to-volume ratio of the pore space of the sandstones. The surface area-to-volume ratio of the pore space of each sandstone was determined using a nitrogen gas adsorption technique and helium porosimetry. kappa ' also exhibits a strong dependence on S w . kappa ' increases rapidly with S w at low saturations, up to some critical saturation above which kappa ' increases more gradually and linearly with S w . Using the surface area-to-volume ratios of the sandstones, the critical saturation in the dielectric response was found to correspond to water coverage of approximately 2 nm on the surface of the pore space. Our interpretation of the observed dependence of kappa ' on both frequency and S w is that it is the ratio of surface water to bulk water in the pore space of a sandstone that controls the dielectric response through a Maxwell-Wagner type of mechanism.