A series of visual experiments were carried out to rate the similarity of color appearance of two color stimuli on categorical and continuous semantic rating scales. Pairs of color stimuli included two copies of the same colored real or artificial object illuminated by a test light source and a reference light source. A formula was developed to predict a category of color similarity (e.g., moderate or good) from an instrumentally measured color difference. Given a numeric value of a color difference between the two members of a pair of colors, for example, 2.07, the formula is able to predict a category of color similarity, for example, good. Because color-rendering indices are based on color differences, the formula could be applied to interpret the values of the new color-rendering index (n-CRI or CRI2012) in terms of such semantic categories. This semantic interpretation enables nonexpert users of light sources to understand the color-rendering properties of light sources and the differences on the numeric scale of the color-rendering index in terms of regular language. For example, a numeric value of 87 can be interpreted as good. (c) 2013 Wiley Periodicals, Inc. Col Res Appl, 39, 252-262, 2014; Published online 14 March 2013 in Wiley Online Library (). DOI 10.1002/col.21798