The revolution you're talking about won't be powered by well-wishes or symbolic purchases. That's actually worse than nothing, because it results in failed installations, wasting resources and disillusioning people about the new technologies.
No, it requires actual knowledge and skillful application of craft.
Start by identifying the equipment you do have
You don't have a water heater. You have a hydronic system that is gas-fired, and that system both heats the house and heats your water. Hydronic systems are able to use radiators or baseboard water-fed heaters. However it also might have an air handling system which circulates heated/cooled air throughout the house. Since hydronic systems cannot provide air conditioning, the house must have a separate A/C approach, and that would need air handling because air conditioning doesn't work with radiators.
So, status quo ante, you have three systems that either are interconnected, or will be:
- Water heating
- House heat
- House air conditioning
So far, your proposal is to rip out only the water heater, and convert it to resistive electric heating. That will leave a mish-mash of scattered tech behind, including 2/3 of a gas hydronic system and That 70's air conditioner. And I'm guessing that proposal is because that's the only thing you know so far.
The math on resistive electric heating
OK, so let's take a look at that water heating requirement and do some math. A "BTU" is the scientific unit for the energy it takes to raise 1 pound of water 1 degree F. (the output of various furnaces and the like are called "BTUs" but are actually BTU/hour).
Suppose our recovery rate is 1 gallon per hour (bear with me). 1 gallon of water weighs 8.33 pounds. Taking cool 50F water off the street and raising it to a bacteria-safe 140F requires 90 degrees rise. Well, 8.33 x 90 is 750 BTU. 1 watt-hour is 3.41 BTUs. So 1 gallon per hour needs 220 watt-hours per hour... or more simply: 1 gallon per hour recovery needs 220 watts.
25 gallons per hour recovery needs 220 x 25 == 5500 watts. Which happens to be exactly the watt rating of your common everyday electric water heater. It works out to 23 amps. (which is derated 125% to 28.75A, and that just fits on a 30A breaker. Imagine that.)
Now, your oddly specific 116.36 GPH recovery rate, you need 25,600 watts, or 106.66 amps. Derated, that takes 133.33 amps, leaving little remaining room on a 200A service. Realistically, that won't fit on a 200A service with your other stuff. You'll need a "Class 320" 400A service to power this and your other electric ambitions, which is real money. By the way, the hydronic system goes in the trash in this scenario. Electric can provide heat directly in the same locations as the radiators.
But even so, this is yesterday's news. And you will not like the electric bill if you do it this way.
Method 1: New style heat pumps
Air conditioning is the wildcard here. What's maddening about North American practice is air conditioning systems is almost a heat pump - which is an essential aspect of the next-gen tech that you want.
This is a superb explainer, and you have to watch it. OK?.
I bet you didn't know air conditioners only needed one more valve to do that trick.
Modern heat pumps are stupidly more efficient than classic air conditioners, and that too is why they're part of the solution. Heat pumps let you tick two boxes: a) heating and b) air conditioning.
The usual heat pump involves using air handling (not radiators) because the air conditioning mode requires air handling.
That crosses off hydronic systems, but we can still score a win with water heating, because They make "heat pump" water heaters too. The normal heat pump water heater takes heat from the utility room, so you'll need to heat that room to effectively put that heat into the water.
Or method 2: a ground sourced heat pump
This is a special type of heat pump that eliminates the big evaporator/condenser unit outside... as well as most of its noise. It is not interchanging heat with the fickle ambient air... but rather, the more stable earth temperature.
Here is an explainer on that.
This happens one of two ways: Either you use a well to pump water out of the earth (and return it some distance away via another well)... or you bury a bunch of coolant loops and run antifreeze through them.
This works more efficiently because the ground source is cooler in summer and warmer in winter than the ambient air.
...And keep your hydronic system
They make heat pumps specifically for hydronic systems. You can get ones which interchange with ambient air, or that interchange with a ground source.
So, you replace the "gas boiler" component with a heat pump unit, and nothing else changes.
A hydronic, ground-sourced system is the "best of all worlds (but one)" system. It is the only system that allows the hot water heater to source energy externally.
What's more, because ground-sourced systems are efficient year-round, there simply is no need for expensive resistive "emergency heat", and that means you don't need 400A electrical service.
However, again, you need an air handler to make air conditioning work.
They solved that problem
Older heat pumps had a problem: they could not work in the very cold, and so they required those expensive resistive "toaster heaters" to heat the house during those times. A friend in the northern US has an older heat pump system that used 30A for the heat pump, *but 140A for the "emergency heat" resistive heating. Yikes! That reason alone forced my friend into 400A service. (you may recall this happened in Texas; all those heat pump systems calling for emergency heat made it impossible for the electric grid to recover.)
Newer heat pumps solve this one of two ways:
- Ground-sourcing, where the ground is always temperate; or
- A much wider operating range, due to better refrigerant choices, and better electronic controls, which make it easy to have a a "self-defrosting" cycle.