Not as many as you think, a water heater only has 3 times the electrical capacity of a standard wall outlet. So probably less than 6 Keurigs, but you'd need them on three (or more) separate circuits otherwise you'd blow the breakers.
If we're looking into their heating capacity they should be able to heat approximately 7 and 1/2 gallons of water an hour. A lower end water heater can supply about 85 gallons of water per hour so you'd need about 11 of them to meet a small house capacity.
If we're looking at their water holding capacity and power consumption. The average house has a 40-60 gallon water heater and a Keurig has a 48oz reservoir. You would need 107 to get to a 40 gallons capacity. When heating they use 1500 watts according to the Internet, so you'd need 160,500 watts (or 1,345.75 amps) of Keurigs to be the equivalent of a low end water heater for a house. The average 40 gallon heater uses between 4500 and 5500 watts.
There's another saying 34 equating it to a tank less heater.
The original question is too vague - there's no one to one mapping between keurigs and water heaters. If you're just trying to heat your houses hot water, any of those answers are valid. So is "1", but it'd be slow and you'd only get a half gallon before refilling it, and at that point the last batch is cold, but it's still heating water... . It's just a question of what you REALLY want and what your constraints are.
If your average house only has one person showering at a time an 18 kW 3.51 GPM Tankless Electric Water Heater would work. It would cost about $500.
To replace that with Keurigs would take some work. They draw 900 to 1500 watts depending on model. So it would take between 20 and 12 Keurigs to match the power draw. I'm not sure what the inlet/outlet tubing diameters are but it seems some replacement parts labeled 1/4" so that's half a gallon per minute max. You'd need 7 or 8 running in parallel to move enough water. Probably 21 900 watt Keurigs running in groups of 3 would come closest.
I estimate about $2000 in Keurigs plus another few hundred dollars in fittings and a lot of time to reproduce a purpose built $500 water heater.
And of course Keurigs break frequently and you'd definitely void any warranty.
Okay SO, this depends on if you can refill them with your water line continually or not. I’m assuming yes as otherwise someone’s answered a swap from a 40 gallon heater.
They do about 12oz in a minute from a quick Google.
Normal tankless water heater is about 3gal/minute. Which is about 400oz.
So, 400/12 gives is 33.33, so since we probably want to make sure we hit at least that, I’d round up to 34. Would need a LOT more electricity for that, as noted by another poster below. Probably more than is actually run to most houses.
Note: unsure how it’ll run without coffee in it, the flow is likely improved and thus you could possibly cut it down by quite a lot, especially with some modification to allow it to flow directly from the heating source in the keurigs you could definitely cut it down.
A normal tankless is 3gal/min? That seems kinda low. Mine does 8 gal/min, but I did zero research. I just happened to move into a place that already had one.
To be honest I’d check mine but I’m out of state right now, Google said normal is 2-5 so I figured 3 is probably fine for most “normal” houses, but idk. For me normal is really as long as I can run a hot shower and a dish washer at the same time.
Checking online says mine is 1.8-4.3 depending on inlet temperature. Though I live in florida, so I likely get the higher end. Looked up average flow for one shower is like 2.2ish, so 4-5 might be more normal.
Soooo, if you want say 2 showers, let’s call it 4.7
Makes 626.1711/12, gives 52.2, so yeah again round up to be sure and we get 53 for a uh, family size house?