Water Heater Efficiency Calculator Formula

Understand the math behind the water heater efficiency calculator. Each variable explained with a worked example.

Formulas Used

Annual Water Heating Cost

annual_cost = annual_btu / 3412 * fuel_cost

Daily Energy Needed

daily_btu = btu_needed / energy_factor

Monthly Cost

monthly_cost = annual_btu / 3412 * fuel_cost / 12

Heat Pump WH Savings (UEF 3.5)

heat_pump_savings = annual_btu / 3412 * fuel_cost - (btu_needed * 365 / 3.5) / 3412 * fuel_cost

Variables

VariableDescriptionDefault
daily_hot_galDaily Hot Water Usage(gallons)50
temp_riseTemperature Rise(degrees F)60
energy_factorEnergy Factor (UEF)(ratio)0.92
fuel_costFuel Cost(USD/therm or USD/kWh)0.15
btu_neededDerived value= daily_hot_gal * temp_rise * 8.33calculated
annual_btuDerived value= btu_needed * 365 / energy_factorcalculated

How It Works

How to Calculate Water Heater Costs

Water heating is typically the second largest energy expense in a home (14-18% of energy bills).

Formula

Daily BTU = Gallons * Temp Rise * 8.33

Annual Energy = Daily BTU * 365 / Energy Factor

Energy Factors

  • Standard gas: 0.60-0.70
  • High-efficiency gas: 0.80-0.98
  • Electric resistance: 0.90-0.95
  • Heat pump water heater: 2.0-4.0
  • Worked Example

    50 gal/day hot water, 60F temp rise, 0.92 energy factor, $0.15/kWh.

    daily_hot_gal = 50temp_rise = 60energy_factor = 0.92fuel_cost = 0.15
    1. 01Daily BTU: 50 * 60 * 8.33 = 24,990 BTU
    2. 02Daily energy with EF: 24,990 / 0.92 = 27,163 BTU
    3. 03Annual energy: 27,163 * 365 = 9,914,526 BTU
    4. 04Annual cost: 9,914,526 / 3,412 * $0.15 = $436