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Tankless cost calculator

A tankless electric is the most expensive way to heat water, and for average family of 4, costs $100 more per year to operate than tank-type heater.
A tankless gas costs more to heat each gallon of water than typical tank-type gas water heater. The only way a tankless saves money vs tank heater, is by lowering consumption. This means that a home with less usage, for example a 1-person home, then the tankless gas heater will save money.
Resource: Side-by-side comparison .pdf
The promise of endless hot water is not consistent with saving money.
Endless hot is not possible with very cold incoming water in winter. Why? the tankless has a limited amount of heat that it can add to cold water as the water rushes past in a pipe. This means that a tankless might be able to support a shower and a faucet running at same time during the summer ... but only support a shower in winter.
Shower heads and showers that consume large volumes of hot water to simulate someone standing in the rain, cannot be supplied by tankless. In some cases, two or three tankless units manifolded together might be able to keep up in summer, but incoming cold water in winter will limit the amount of hot that can be supplied.
For there type showers, a tank-type condensing heater might be better choice. Or installing two or three ordinary tank type heaters.
Resources:
Review Polaris condensing heater  
Two water heaters
This comparison is NOT a true reflection of energy use over time; only the costs to heat one tank of water from a cold start.
Heating tank from cold start would only be when tank is new or when service is interrupted


Estimates made are for new water heater in perfect operating environment.
Calculations do not consider longer-term effects of hard water, inefficiencies caused by high temperature settings, fluctuating temperature of incoming water.
Natural Gas daily cost
Volume of   Temperature BTUs EF rating BTUs   Actual
Hot Water H2O Weight rise in required of the purchased Cost per daily cost to
Heated   degrees F to water heater to heat therm heat the 
      heat water   water   water **
64 8.33 77 41,050 0.62 66,210 $1.2000 $0.795
Electric
Volume of   Temperature BTUs EF rating BTUs   Actual
Hot Water H2O Weight rise in required of the purchased Cost per daily cost to
Heated   degrees F to water heater to heat KW/hour heat the 
      heat water   water   water **
64 8.33 77 41,050 0.94 43,670 $0.0841 $1.076
Propane Gas
Volume of   Temperature BTUs EF rating BTUs Cost per Actual
Hot Water H2O Weight rise in required of the purchased gallon daily cost to
Heated   degrees F to water heater to heat propane heat the 
      heat water   water   water **
64 8.33 77 41,050 0.62 66,210 $1.2100 $0.875
Tankless
Volume of   Temperature BTUs EF rating BTUs Cost per Actual
Hot Water H2O Weight rise in required of the purchased gallon daily cost to
Heated   degrees F to water heater to heat propane heat the 
      heat water   water   water **
64 8.33 77 41,050 0.82 50,061 $1.2000 $0.656

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