Federated learning is a recent trend in the field of machine learning for building a collaborative model from distributed data while preserving its privacy. The focus of existing literature is on developing supervised federated learning algorithms requiring labeled data. Whereas only a few solutions have been proposed to identify patterns in distributed unlabeled data using federated clustering methods. However, the issue of measuring the goodness of clusters remains unsolved as existing cluster validity indices cannot be applied in federated learning due to the unavailability of the entire data. To fulfill this research gap, a new metric called FedCI is proposed in the paper for measuring the performance of federated clustering methods, The rationale for FedCI is also discussed and the new metric is validated by comparing it with DB index and Silhouette score. It is found that the behavior of FedCI is consistent with existing metrics. Further, FedCI is applied to the recently proposed FedCLUS a federated clustering method. The FedCLUS algorithm has distinctive characteristics like identification of arbitrarily shaped clusters; the ability to merge, split and discard clusters reported by data owners; communication cost effectiveness. The performance of FedCLUS is compared with centralized DBSCAN using FedCI on various datasets. The results indicate that FedCLUS performs close to the centralized DBSCAN clustering algorithm. The FedCI is expected to guide in finding better clusters in federated settings.