This article gives an overview of sample size calculations for a single response and a comparison of two responses in a parallel group trial where the outcome is binary. Sample size derivation is given for trials where the objective is to demonstrate: superiority, equivalence, non-inferiority and estimation to a given precision. For each type of trial the null and alternative hypotheses are described and how the impact these have on the sample size calculations. For each type of trial the calculations are highlighted through worked examples. Sample size tables for the different types of trials and worked examples are given to assist in future calculations. Copyright © 2012 John Wiley & Sons, Ltd.