Abstract: Apparatuses of an energy efficient water heater and methods for controlling the same are disclosed. In one embodiment, a water heater may include a water inlet configured to receive input water, an input water temperature sensor configured to detect a temperature of the input water, a user interface unit configured to receive an output water temperature setting selected by a user, a controller configured to determine a flow rate of an output water based on the input water temperature and the output water temperature setting, a heating unit configured to heat the input water to produce the output water, the controller is further configured to control the heating unit and a proportional flow restrictor to produce the flow rate of the output water, and a water outlet configured to transfer the output water at the flow rate of the output water.