Human perception of self-motion is the result of combining information from many sensory systems such as visual, vestibular, and proprioceptive systems. Research on vestibular thresholds has mainly focused on estimating absolute thresholds for translational and rotational motions and estimating difference thresholds for rotational velocities. In this study, psychophysical methods are used to determine the ability of normal subjects to discriminate among sinusoidal accelerations in the horizontal plane. Difference thresholds were estimated using four different acceleration amplitudes ranging from peak amplitude of 0.5-2.0 m/s2 and three different frequencies ranging from 0.25 to 0.6 Hz. Difference thresholds ranged from 0.05 m/s2 for a sinusoidal acceleration with peak amplitude of 0.5 to 0.13 m/s2 for a sinusoidal acceleration with peak amplitude of 2.0 m/s2. The relationship between difference threshold estimates and peak accelerations is found to compare favorably to Weber's law, which is often used to represent changes in threshold values in other sensory systems. Moreover, the threshold estimates tend to decrease as frequency increases. The effect of visual condition on thresholds was also investigated. It was shown that when the visual scene is stationary with respect to the subject, there are no significant differences between threshold estimates based on closed-eye and open-eye scenarios.