This is how the computations are made to determine how much it costs to heat a house with a gas furnace and an electric heat pump. You can click on a term to go to its definition. ( The asterisk (*) is used here as the symbol for multiplication, and the forward slash (/) as the symbol for division)

Gas Furnace

For a gas furnace, first we calculate the Annual Energy Consumption (AEC). Annual Energy Consumption, in Therms per year, is estimated as:

AEC = 0.77 * DHR * (1.20 / 1.15) * HLH * 100 *(1/100,000) * (1 / AFUE)

This equation is derived from the Gas Appliance Manufacturers Association (GAMA) procedure for estimating the annual heating requirements an comparing the costs of operation of different models. The factor of 0.77 is an adjustment factor taken from the DOE test procedure which serves to adjust the calculated design heating requirement and heating load hours to the actual heating load likely to be experience by a heating system.

The factors 1.20 and 1.15 come from Table 7A in ACCA Manual J - Load Calculations. They represent "duct loss multipliers" - heat lost when ducts insulated to R-4 are exposed to outdoor ambient temperatures. Gas furnaces with supply temperatures above 120 deg F have a duct loss multiplier of 1.20. Heat pumps have supply temperatures below 120 deg F, giving them a duct loss multiplier of 1.15. The model in Manual J assumes supply temperatures below 120 degrees, so the factor, (1.20 / 1.15) corrects the model for the higher heat losses in the ducts of gas heating systems.

The factor of 100 in the gas furnace AEC equation converts AFUE from percent to decimal form.

The factor of 1/100,000 in the gas furnace AEC is the heating value for natural gas, in Btu/Therm, assuming 1 ccf = 1 Therm.

Estimated annual fuel cost = AEC * Fuel cost, in dollars/Therm.

If the gas furnace has a standing pilot light, there will be an additional fuel use of about 70 Therms per year. This is multiplied by the fuel cost per Therm and added to the estimated annual fuel cost.

The cost of running the blower will average about 7% to 12 % of fuel cost. 10% is added as a reasonably close estimate.

The customer will probably be charged an additional monthly charge by the gas company. If the customer doesn't have gas now, the additional monthly charge for 12 months should be added to the annual cost. It can be as much as $144 or more! Sometimes this charge is called an "availability charge", "base use charge", customer charge", or "service charge."

Electric Heat Pump

For an electric heat pump, Annual Energy Consumption (AEC), in kWh/year, is estimated as:

AEC = .77 * DHR * HLH * 0.001 * (1 / HSPF)

The factor 0.001 is the number of watts in a kilowatt.

Estimated annual fuel cost = AEC * Fuel cost, in dollars/kilowatt-hour.

Terms and Definitions

DHR

Design Heating Requirement of a building (from Manual J). To estimate DHR for a typical home, multiply the area of the home is square feet by 22 Btu/sq. ft. If the home is well-insulated, use 17 Btu/sq. ft. If the home is poorly insulated, use 27 Btu/sq. ft.

HLH

Heating Load Hours. See Typical Winter Heating Load Hours.

HSPF

Heating Seasonal Performance Factor, in Btu/watt-hours, based on the DOE test procedure. The appropriate factor to use can be obtained from your dealer, from the ARI directory, or from the Energy Guide label on the heat pump.

AFUE

The Annual Fuel Utilization Efficiency, in percent. This is found in the Gas Appliance Manufacturers Association (GAMA) directory, or on the Energy Guide label on the furnace.