Gaze information has been used in numerous fields such as cognitive psychology research, input interfaces, and intelligent transport systems. In this study, we focused on electro-oculographic methods because of the low level of inconvenience to users, and developed a simple method for gaze estimation based on planar approximations of the voltage ratios (Vr) calculated from multiple electro-oculogram signals. The results suggest that Vr can be used for estimating gaze without being affected by the drift phenomenon that reduces the estimation accuracy. Numerical experiments using an eyeball battery model reveal that the proposed method can be used in yaw and pitch ranging from −40° to 40° and −30° to 30°, respectively, with an estimated error of approximately 3.5°, using at least nine electrodes arranged in an L shape.