Three different Bayesian approaches to sample size calculations based on highest posterior density (HPD) intervals are discussed and illustrated in the context of a binomial experiment. The preposterior marginal distribution of the data is used to find the sample size needed to attain an expected HPD coverage probability for a given fixed interval length. Alternatively, one can find the sample size required to attain an expected HPD interval length for a fixed coverage. These two criteria can lead to different sample size requirements. In addition to averaging, a worst possible outcome scenario is also considered. The results presented here provide an exact solution to a problem recently addressed in the literature.