Estimated time contracts or dilates depending on many visual-stimulation attributes (size, speed, etc.). Here we show that when such attributes are jointly modulated so as to respect the rules of perspective, their effect on the perceived duration of moving objects depends on the presence of contextual information about viewing distance. We show that perceived duration contracts and dilates with changes in the retinal input associated with increasing distance from the observer only when the moving objects are presented in the absence of information about the viewing distance. When this information (in the form of linear perspective cues) is present, the time-contraction/dilation effect is eliminated and time constancy is preserved. This is the first demonstration of a perceptual time constancy, analogous to size constancy but in the time domain. It points to a normalization of time computation operated by the visual brain when stimulated within a quasi-ecological environment.