An analysis of the effective radii of vacancies and the stoichiometric expansion coefficient is performed on metal oxides with fluorite and perovskite structures. Using the hard sphere model with Shannon ion radii we find that the effective radius of the oxide vacancy in fluorites increases with increasing ion radius of the host cation and that it is significantly smaller than the radius of the oxide ion in all cases, from 37 % smaller for HfO2 to 13 % smaller for ThO2. The perovskite structured LaGaO3 doped with Sr or Mg or both is analyzed in some detail. The results show that the effective radius of an oxide vacancy in doped LaGaO3 is only about 6 % smaller than the oxide ion. In spite of this the stoichiometric expansion coefficient (a kind of chemical expansion coefficient) of the similar perovskite, LaCrO3, is significantly smaller than the stoichiometric expansion coefficient of the fluorite structured CeO2. Our analysis results indicate that the smaller stoichiometric expansion coefficient of the perovskites is associated with the restraining action of the A-O sub-lattice to dimensional changes in the B-O sub-lattice and vice versa.