Two methods to transform primary chromaticities and white point into primary tristimulus values are examined and compared. One method appears in numerous places in the literature; we refer to this as the "familiar" method, and provide a novel interpretation of it. The second is much less well-known and is referred to as the "unfamiliar" method. Necessary and sufficient conditions for computing primary tristimulus values from their chromaticities are identified; in brief, the triangle in the (x, y) chromaticity diagram must have non-zero area. The computational burdens for the methods were compared; the familiar method required slightly more arithmetical operations. Two problems with the familiar method were identified: high potential for rounding error and the inability to contend with a non-luminous primary. The unfamiliar method is less prone to rounding error, and is able to contend with primaries on the alychne. It is recommended that the unfamiliar method be preferred.