A water heating system can include a water heater having a tank, and a first temperature sensor disposed toward a top end of the tank to measure a first temperature and a second temperature sensor disposed toward a bottom end of the tank to measure a second temperature. The water heating system can further include a controller communicably coupled to the first temperature sensor and the second temperature sensor, where the controller determines an amount of heated water in the tank based on a plurality of algorithms and measurements made by the first and second temperature sensors. The plurality of algorithms solves for at least one calculated temperature for at least one point between a first location of the first temperature sensor and a second location of the second temperature sensor, where the at least one calculated temperature is used to determine the amount of heated water in the tank.

A tank-type water heater includes a storage tank and a heating circuit outside of the tank. The heating circuit includes at least one heat engine and at least one pump for circulating water from the bottom of the tank through the heat engine and back to the top of the tank. A stratifier introduces the heated water from the heating circuit into the top of the tank in a diffuse manner to promote stratification of hot water in the tank.

A water heating system can include a water heater having a tank, and a first temperature sensor disposed toward a top end of the tank to measure a first temperature and a second temperature sensor disposed toward a bottom end of the tank to measure a second temperature. The water heating system can further include a controller communicably coupled to the first temperature sensor and the second temperature sensor, where the controller determines an amount of heated water in the tank based on a plurality of algorithms and measurements made by the first and second temperature sensors. The plurality of algorithms solves for at least one calculated temperature for at least one point between a first location of the first temperature sensor and a second location of the second temperature sensor, where the at least one calculated temperature is used to determine the amount of heated water in the tank.

A water heating system can include a water heater having a tank, and a first temperature sensor disposed toward a top end of the tank to measure a first temperature and a second temperature sensor disposed toward a bottom end of the tank to measure a second temperature. The water heating system can further include a controller communicably coupled to the first temperature sensor and the second temperature sensor, where the controller determines an amount of heated water in the tank based on a plurality of algorithms and measurements made by the first and second temperature sensors. The plurality of algorithms solves for at least one calculated temperature for at least one point between a first location of the first temperature sensor and a second location of the second temperature sensor, where the at least one calculated temperature is used to determine the amount of heated water in the tank.

A water heater including a storage tank including a water inlet and a water outlet, a pump, an upper temperature sensor, a lower temperature sensor, and an electronic processor. The electronic processor is configured to receive an upper temperature signal and a lower temperature signal, compare the upper temperature signal to a sum of a setpoint temperature threshold minus a temperature differential, and compare the lower temperature signal to a high limit temperature threshold. The electronic processor is further configured to activate the pump in response to the first upper temperature signal being less than the sum of the setpoint temperature threshold minus the temperature differential and the first lower temperature signal being less than the predetermined high limit temperature threshold.

A tank-type water heater includes a storage tank and a heating circuit outside of the tank. The heating circuit includes at least one heat engine and at least one pump for circulating water from the bottom of the tank through the heat engine and back to the top of the tank. A stratifier introduces the heated water from the heating circuit into the top of the tank in a diffuse manner to promote stratification of hot water in the tank.

A water heater including a storage tank including a water inlet and a water outlet, a pump, an upper temperature sensor, a lower temperature sensor, and an electronic processor. The electronic processor is configured to receive an upper temperature signal and a lower temperature signal, compare the upper temperature signal to a sum of a setpoint temperature threshold minus a temperature differential, and compare the lower temperature signal to a high limit temperature threshold. The electronic processor is further configured to activate the pump in response to the first upper temperature signal being less than the sum of the setpoint temperature threshold minus the temperature differential and the first lower temperature signal being less than the predetermined high limit temperature threshold.

A water heating system can include a water heater having a tank, and a first temperature sensor disposed toward a top end of the tank to measure a first temperature and a second temperature sensor disposed toward a bottom end of the tank to measure a second temperature. The water heating system can further include a controller communicably coupled to the first temperature sensor and the second temperature sensor, where the controller determines an amount of heated water in the tank based on a plurality of algorithms and measurements made by the first and second temperature sensors. The plurality of algorithms solves for at least one calculated temperature for at least one point between a first location of the first temperature sensor and a second location of the second temperature sensor, where the at least one calculated temperature is used to determine the amount of heated water in the tank.