According to an embodiment, an estimation apparatus includes first to fourth obtainers and an estimator. The first obtainer obtains, for each slave node, a piece of synchronization information in a network configuration including: nodes including a master node serving as a time synchronization source, one or more slave nodes serving as time synchronization destinations, and relay nodes; and paths connecting the nodes. The second obtainer obtains, for each path, a piece of band information. The third obtainer obtains, for each path, a piece of traffic information. The fourth obtainer obtains, for each relay node, a piece of path information. The estimator estimates a predetermined relay node causing reduction of accuracy of time synchronization between the master node and the one or more slave nodes, based on the one or more pieces of synchronization information, the pieces of band information, the pieces of traffic information, and the pieces of path information.