The absolute contrast ratio of a display is a distinctive measure of the display contrast. However, this contrast ratio does not match the perceived contrast as it only uses the physical characteristic of the display. Therefore, this paper proposes a contrast measure that considers the perceptually discriminable brightness within the display brightness ranges. First, the Weber-Fechner ratio is applied to determine the brightness ranges of the display gamut in CIECAM02. Thereafter, the number of brightness values for each brightness range is computed and the perceptually discriminable brightness is then estimated based on the sum of the ratio between the number of brightness values in each brightness range and the brightness length in the display gamut. A preference test was conducted on various displays using random brightness patches to evaluate the perceived contrast. Experimental results showed that the proposed measure is more consistent with human perception than previous contrast measures.