In medical research, while reporting the results for cluster randomized trial, intra-class correlation coefficient estimates must be provided along with standard error to account for calculation of sample size to achieve the desired power. In the present article, an attempt is made to derive the standard error of analysis of variance estimates of intra-class correlation coefficient for unbalanced nested design with almost no distributional assumptions. To fulfill the gap of strong need of distributional assumptions, balanced design for ease of calculation, equality of variances between clusters and large sample, there was a need of general formula for standard error of intra-class correlation coefficient which can be deployed in multicentre clinical trials. One simulation study is carried on to assess the behavior of significant constants and validity of formula over varying cluster sizes as well as varying number of clusters.