It is often necessary to compare two measurement methods in medicine and other experimental sciences. This problem covers a broad range of data. Many authors have explored ways of assessing the agreement of two sets of measurements. However, there has been relatively little attention to the problem of determining sample size for designing an agreement study. In this paper, a method using the interval approach for concordance is proposed to calculate sample size in conducting an agreement study. The philosophy behind this is that the concordance is satisfied when no more than the pre-specified k discordances are found for a reasonable large sample size n since it is much easier to define a discordance pair. The goal here is to find such a reasonable large sample size n. The sample size calculation is based on two rates: the discordance rate and tolerance probability, which in turn can be used to quantify an agreement study. The proposed approach is demonstrated through a real data set.