Objective This study aims to address the challenge of privacy-preserving Alzheimer’s disease classification using federated learning across various data distributions, focusing on real-world applicability. The goal is to improve the efficiency of classification by minimizing communication rounds between clients and the central server. Methods The proposed approach leverages two key strategies: increasing parallelism by utilizing more clients in each communication round and increasing computation per client during the intervals between rounds. To reflect real-world scenarios, data is divided into three distributions: identical and independently distributed, non-identical and independently distributed equal, and non-identical and independently distributed unequal. The impact of extreme quantity distribution skew is also examined. A convolutional neural network is used to evaluate the performance across these setups. Results The empirical study demonstrates that the proposed federated learning approach achieves a maximum accuracy of 84.75%, a precision of 86%, a recall of 85%, and an F1-score of 84%. Increasing the number of local epochs improves classification performance and reduces communication needs. The experiments show that federated learning is effective in handling heterogeneous datasets when all clients participate in each round of training. However, the results also indicate that extreme quantity distribution skew negatively impacts classification performance. Conclusions The study confirms that federated learning is a viable solution for Alzheimer’s disease classification while preserving data privacy. Increasing local computation and client participation enhances classification performance, though extreme distribution imbalances present a challenge. Further investigation is needed to address these limitations in real-world scenarios.