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A 50 gallon electric water heater tank is a cylinder about 16 inches in diameter and 5 feet tall. The cylinder has a surface area of 60 * 16 * 3.14 + 2 * 16 * 16 * 3.14 / 4 * 2 or around 3300 square inches. Call it 23 square feet. If the water temperature is 125 degrees and the ambient is 40 degrees and the insulation is R11 then the heat loss is 23 * (125 - 40) / 11 or 178 BTU per hour there are 24 * 30 hours in a month, so the heat loss is 178 * 24 * 30 = 128000 BTU per month There are 3413 BTU per kilowatt hour, so we use 37.5 KWH to replace the lost heat. (Electric heaters are 100 percent efficient). At 0.08 dollars per kilowatt hour, we have $3.00 per month. That's where I got the number I quoted. Several of these assumptions may be optimistic. Assume the water heater is miserable cheap one insulated only to R4, and the water temperature is a toasty 140 degrees. Under these conditions we use 3 times as much energy to maintain the temperature, but that is still only $9.00 per month, or $18.00 per month per two water heaters. (I have neglected conductive loss to the piping, but I don't think this amounts to much). For a situation in Florida, the average ambient would be more like 60 degrees, which would make the heat loss more like $16.00 per month. I cannot explain the $30.00 per month that you measured. Maybe you have a leaky faucet? Or maybe there was something wrong with how you did the measurement? My own anecdotal experiences come from shops and houses sitting idle with the water heater left on. The only thing spinning the electric meter is the standby loss. At the end of the month it is easy enough to read the electric bill and observe the cost of the hot water sitting there unused. The figures I have seen are more consistent with the $3.00 to $8.00 range.
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