This paper introduces subject granular privacy in the Federated Learning (FL) setting, where a subject is an individual whose private information is embodied by several data items either confined within a single federation user or distributed across multiple federation users. We formally define the notion of subject level differential privacy for FL. We propose three new algorithms that enforce subject level DP. Two of these algorithms are based on notions of user level local differential privacy (LDP) and group differential privacy respectively. The third algorithm is based on a novel idea of hierarchical gradient averaging (HiGradAvgDP) for subjects participating in a training mini-batch. We also introduce horizontal composition of privacy loss for a subject across multiple federation users. We show that horizontal composition is equivalent to sequential composition in the worst case. We prove the subject level DP guarantee for all our algorithms and empirically analyze them using the FEMNIST and Shakespeare datasets. Our evaluation shows that, of our three algorithms, HiGradAvgDP delivers the best model performance, approaching that of a model trained using a DP-SGD based algorithm that provides a weaker item level privacy guarantee.