Computation offloading at lower time and lower energy consumption is crucial for resource limited mobile devices. This paper proposes an offloading decision-making model using federated learning. Based on the task type and the user input, the proposed decision-making model predicts whether the task is computationally intensive or not. If the predicted result is computationally intensive, then based on the network parameters the proposed decision-making model predicts whether to offload or locally execute the task. According to the predicted result the task is either locally executed or offloaded to the edge server. The proposed method is implemented in a real-time environment, and the experimental results show that the proposed method has achieved above 90% prediction accuracy in offloading decision-making. The experimental results also present that the proposed offloading method reduces the response time and energy consumption of the user device by ~11-31% for computationally intensive tasks. A partial computation offloading method for federated learning is also proposed and implemented in this paper, where the devices which are unable to analyse the huge number of data samples, offload a part of their local datasets to the edge server. For secure data transmission, cryptography is used. The experimental results present that using encryption and decryption the total time is increased by only 0.05-0.16%. The results also present that the proposed partial computation offloading method for federated learning has achieved a prediction accuracy of above 98% for the global model.