Is an air water heater more energy efficient than an electric water heater?

Since there is some scientific basis for saying that it saves electricity, your calculations are good. But the consumption of electricity is not to heat the water. The principle of air energy to show you, you know. There is a refrigerant gas-liquid interconversion.

The host compressor by consuming part of the electricity, the low-temperature, low-pressure refrigerant gas (usually R22 refrigerant) compressed into high-temperature, high-pressure gas, high-temperature, high-pressure gas through the condenser (commonly known as a heat exchanger, built into the host) to release heat to heat the water, their own temperatures are lowered, after throttling through the expansion valve pressure drop, into a low-temperature, low-pressure gas-liquid mixtures, in the evaporator. In the evaporator, the refrigerant absorbs the heat in the air and becomes a low-temperature, low-pressure gas, which is then absorbed by the compressor and compressed into a high-temperature, high-pressure gas to heat the hot water. This cycle is repeated to achieve from the air to absorb heat released into the water.

This process uses a dual-cycle system, in which the refrigerant cycle, that is, the refrigerant gas through the closed tube in the host compressor and the host built-in heat exchanger cycle. Water circulation, in order to ensure the efficiency of the refrigerant cycle of the water tank water through the water pump in the water tank and heat exchanger between the cycle.