The structural, energetic, and thermodynamic properties of the Co_{3 – s}Al_sO₄ (s = 0, 1, 2, and 3) crystal family are studied using periodic DFT calculations. We provide a quantitative discussion of the cation distribution effect on the cell parameter, the oxygen Wyckoff position, the interatomic distances and the energies of the structures. It is demonstrated that the low cobalt containing CoAl₂O₄ spinel is the most stable structure of the Co_{3 – s}Al_sO₄ (s = 0, 1, 2, and 3) crystal family.