The dynamic range of the human visual system should be an important parameter in the design of high dynamic range (HDR) display devices. A good display should at least approximate this range. However, the literature reports a simultaneous dynamic range between 2 and 4 log units of luminance, leaving ambiguity as to what dynamic range HDR display devices should cater for. In this paper we present a sequence of psychophysical experiments, carried out with the aid of a high dynamic range display device, to determine the simultaneous dynamic range of the human visual system under full adaptation to a given background luminance. Our findings show that the human visual system is capable of distinguishing contrasts over a range of 3.7 log units under specific viewing conditions. Further, we show how the dynamic range is affected by stimulus duration, contrast of the stimulus as well as background illumination, thereby accounting for the differences reported in the literature and providing guidance for display design.