I found this site Ask Mr. Electricity that has a calculation of how much it costs to heat water with a hot water heater.
Bottom line is that given their calculations, it costs about 1¢ to 2¢ to heat a gallon of water.
The exact amount will depend on the efficiency of your hot water heater, whether you use gas or electric and exactly what your electric or gas costs are.
From the Ask Mr. Electricity site:
"Energy required to heat a tank of water
- A Btu, or British thermal unit, is the amount of energy needed to raise one pound of water from 60°F to 61°F at sea level. (Wikipedia)
- A gallon of water weights 8.33 lbs.
- If the incoming water is 60°F and we want to raise it to 123°F, that's a 63°F rise.
- Heating a gallon of water thus requires 8.33 x 63 = 525 Btu's, at 100% efficiency.
Cost to heat water in a gas tank
- A typical gas tank water heater is only 59% efficient. So it takes 525 ÷ 59% = 890 Btu's to heat a gallon of water in a gas tank.
- One therm is 100,000 btu's. So one Btu is 0.00001 therms. (Pacific NW Natl. Lab.)
- 890 Btu's is 0.0089 therms.
- So we've got 0.0089 therms to heat a gallon of water, or 0.0089 x 40 = 0.356 therms to heat a 40-gallon tank.
- At $1.42/therm, it costs 0.356 x $1.42 = $0.51 to heat a 40-gallon tank.
- Another source comes up with a similar figure: 0.40 therms for the tank (based on 0.11 therms to heat 11 gallons of water. (Multi-housing Laundry Association)
- MHLA also says it takes 3.3 therms to keep 11 gallons hot for one month.
Cost to heat water in an electric tank
- A typical electric water heater is 90.4 to 95% efficient. Let's call that 92.7% on average.
- So it takes 525 ÷ 92.7% = 566 Btu's to heat a gallon of water in an electric tank.
- One kWh is 3413 Btu's, so one Btu is 0.000293 kWh.
- 566 Btu's x 0.000293 kWh/Btu = 0.166 kWh.
- So we've got 0.166 kWh to heat a gallon of water, or 0.166 x 40 = 6.63 kWh to heat a 40-gallon tank.
- At $0.11/kWh, it costs 6.63 x $0.11 = $0.73 to heat a 40-gallon tank."
The two keys they had were that it cost $0.51 to heat 40 gallons using gas or $0.73 using electric. Thats $0.01275 per gallon for gas and $0.01825 per gallon with electric.