Gamut volume computations in perceptual spaces are useful for optimizing designs of color displays. We develop a useful representation of the gamut of an additive display that facilitates efficient numerical computation of the gamut volume. For three primary systems, our representation coincides with the obvious representation of a three-primary additive gamut, while for multi-primary systems, the representation we develop provides a partition of the device gamut as a disjoint union of displaced three primary gamuts thereby facilitating a computation of the overall gamut volume as the sum of these individual three primary gamut volumes. Based on our representation, we develop and evaluate several alternative numerical schemes for gamut volume computations in perceptual spaces, comparing their accuracy and computational requirements.