In March I concluded that a timed water heater 12 hours On/Off saved 6.25 KwH per month. See Does a water heater timer save, a case study
I have also calculated that my cost to heat water is 1.3606 cents per gallon
When I found myself with an extra water monitor after I upgraded to a Flume water monitor. I placed the extra monitor at the water heater and bumped the gallons used against Sense data to verify these conclusions. I have found the actual cost is 2.06222 cents per gallon. Obviously, the cost to keep the standing water hot is driving this. This does support a tankless heater in my situation over the long haul as I would DIY installation. The average annual savings $74.13
To be fair I have very low water consumption, averaging 23.3 gallon per day per person.
Here is the formula to calculate to cost to heat water:
It takes .000293 Kwh to raise 1 pound of water 1° F
A gallon of water weighs 8.34 lbs.
Average temp tap water for me is 72 degrees
Water heater set at 120 degrees so 48 degrees of rise
Efficiency of heater .95 (95%) For 2015 and later models .90 pre 2015
Ave price of electricity .116 KwH
Formula: .000293 X 8.34 X 48 X .90 X .116 = $.013606 per gallon