It is shown that tristimulus values have been endowed with various dimensions, ranging from power to no dimensions at all. Values of the color-matching functions (which are tristimulus values by one definition) have no dimensions, but can have units in the sense of inches-per-meter. When associated with real primaries, color-matching functions can have the units of power (e.g., watts) of the indicated wavelength per unit power (watt) of the indicated primary. Color-matching functions associated with non-real primaries (such as CIE XYZ) have no units at all. If the color-marching functions are defined to comprise tristimulus weights instead of values, the dimensional inconsistency can be avoided. The indeterminacy of units, on the other hand, is intrinsic to the affine property of color-matching space, and cannot be eliminated.