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Stationarity perception refers to the ability to accurately perceive the surrounding visual environment as world-fixed during self-motion. Perception of stationarity depends on mechanisms that evaluate the congruence between retinal/oculomotor signals and head movement signals. In a series of psychophysical experiments, we systematically varied the congruence between retinal/oculomotor and head movement signals to find the range of visual gains that is compatible with perception of a stationary environment. On each trial, human subjects wearing a head-mounted display execute a yaw head movement and report whether the visual gain was perceived to be too slow or fast. A psychometric fit to the data across trials reveals the visual gain most compatible with stationarity (a measure of accuracy) and the sensitivity to visual gain manipulation (a measure of precision). Across experiments, we varied 1) the spatial frequency of the visual stimulus, 2) the retinal location of the visual stimulus (central vs. peripheral), and 3) fixation behavior (scene-fixed vs. head-fixed). Stationarity perception is most precise and accurate during scene-fixed fixation. Effects of spatial frequency and retinal stimulus location become evident during head-fixed fixation, when retinal image motion is increased. Virtual Reality sickness assessed using the Simulator Sickness Questionnaire covaries with perceptual performance. Decreased accuracy is associated with an increase in the nausea subscore, while decreased precision is associated with an increase in the oculomotor and disorientation subscores.