Primary and secondary O-18 equilibrium isotope effects on the acidities of a variety of Bronsted and Lewis acids centered on carbon, boron, nitrogen, and phosphorus were computed by density-functional theory. For many of these acids, the secondary isotope effect was found to be larger than the primary isotope effect. This is a counterintuitive result, because the H atom that is lost is closer to the (18) atom that is responsible for the primary isotope effect. The relative magnitudes of the isotope effects can be associated with the vibrational frequency and zero-point energy of the X=O vibrations, which are greater than those of the X-O vibrations. However, the difference between these contributions is small, and the major responsibility for the larger secondary isotope effect comes from the moment-of-inertia factor, which depends on the position of the O-18 atom relative to the principal axes of rotation.