COP, AFUE and Delivered Heat: Putting Every Fuel on One Scale

Why this matters

Customers buy heat in four different units: kWh, therms, gallons of propane and gallons of oil. None of those units means the same amount of heat, and none of the equipment turns all of what it buys into heat in the house. An estimator who compares a heat pump quote against a furnace quote without converting both to delivered heat is comparing a price per gallon with a price per pound, and the customer will make a fifteen-year decision on it. Every honest fuel comparison starts with the same conversion, done the same way, and the conversion is short.

Two steps, always in this order

Step one: convert the unit bought into BTU of fuel energy. A BTU (British thermal unit) is the energy that raises one pound of water by one degree Fahrenheit. It is the common currency. See related: What a BTU Actually Is.

Step two: multiply by the equipment's efficiency to get BTU delivered. Delivered heat is what ends up in the house's air or water. Fuel energy that goes up a flue, or that the equipment never captured, was paid for and not received.

The heat contents worth knowing cold, all at the energy actually contained in the fuel:

• 1 kWh = 3,412 BTU. This is a unit conversion, not a measurement, so it does not vary.
• 1 therm = 100,000 BTU. Also a definition.
• 1 ccf of natural gas (100 cubic feet) is close to one therm but not equal to it; the utility applies a therm factor printed on the bill because gas heat content varies by supply. See related: Anatomy of a Natural Gas Bill and the Therm Conversion.
• 1 gallon of propane is about 91,500 BTU and 1 gallon of No. 2 heating oil is about 138,500 BTU, using the U.S. Energy Information Administration's published heat contents, rounded. Both vary slightly with the product.

The efficiency numbers, and what each one means

COP, coefficient of performance, is heat delivered divided by energy used, both in the same units. It is a ratio at one set of conditions, at one moment.

• Electric resistance heat has a COP of 1.0. Baseboard, a space heater, furnace backup strips, an electric boiler: every kWh becomes 3,412 BTU of heat in the house, no more and no less.
• A heat pump's COP is above 1 because it moves heat rather than making it. It uses electricity to pull heat from outdoor air (or the ground) and pump it inside. A COP of 3 means 3,412 x 3 = 10,236 BTU delivered per kWh.
• A heat pump's COP falls as the outdoor temperature falls, because the colder the source air, the harder the compressor works to lift heat out of it. A unit that delivers a COP near 3 or better in mild weather may deliver something nearer 2 in hard cold, with the real figures for that model in the manufacturer's extended performance data at each outdoor temperature. Standard ratings test heating at 47 F and 17 F, and cold-climate equipment also publishes figures at lower outdoor temperatures.

AFUE, annual fuel utilization efficiency, applies to furnaces and boilers burning gas, propane or oil. It is a seasonal fraction from a standard test that includes start-up and cycling losses: an AFUE of 95 means the test found about 95 percent of the fuel energy delivered as heat over a modeled season. AFUE does not count the electricity the blower and inducer use, and it does not count heat lost from ducts or pipes after it leaves the appliance.

HSPF, heating seasonal performance factor, is the heat pump's seasonal rating: BTU delivered per watt-hour across a modeled heating season. Dividing HSPF by 3.412 turns it into a seasonal average COP under that rating's assumptions. HSPF2 is the newer test procedure, which models higher duct resistance, so the same unit gets a lower number under HSPF2 than under HSPF. Divide either by 3.412, but do not compare an HSPF from one with an HSPF2 from the other.

What these ratings are and are not, test by test, is covered in its own card. See related: What an Efficiency Number Actually Compares.

The conversion strip

UNIT BOUGHT       BTU IN     EFFICIENCY   BTU DELIVERED
1 kWh, resist      3,412     COP 1.0           3,412
1 kWh, HP mild     3,412     COP 3.0          10,236
1 kWh, HP cold     3,412     COP 2.0           6,824
1 therm gas      100,000     AFUE 95          95,000
1 therm gas      100,000     AFUE 80          80,000
1 gal propane     91,500     AFUE 95          86,925
1 gal oil        138,500     AFUE 84         116,340

The heat pump COPs and the oil AFUE are illustrative values chosen to show the method; use the figures for the actual equipment. Each row is simply BTU in x efficiency: 91,500 x 0.95 = 86,925; 138,500 x 0.84 = 116,340.

Flip any row to get the units it takes to deliver one million BTU, which is the common yardstick for cost comparison:

• Resistance: 1,000,000 / 3,412 = 293 kWh.
• Heat pump at COP 3.0: 1,000,000 / 10,236 = 98 kWh. At COP 2.0, 147 kWh.
• Gas at 95 AFUE: 10.5 therms. At 80 AFUE: 12.5 therms.
• Propane at 95 AFUE: 11.5 gallons. Oil at 84 AFUE: 8.6 gallons.

Multiply each by the rate on that fuel's bill and you have a cost per million BTU delivered that can be compared across fuels. See related: How to Compare Heating Costs Across Fuels per Million BTU, which owns that comparison and its traps.

Worked example: one season of heat, four ways

A customer with a 20-year-old gas furnace rated 80 AFUE is weighing a heat pump and asks what it would take to heat the house with one. Start from what the house actually used, not from a rule of thumb.

Find the heating therms. Last year's bills total 920 therms. Summer months, with only the water heater and range, average 14 therms a month, so twelve months of that non-heating use is 14 x 12 = 168 therms. Heating used 920 - 168 = 752 therms. Call it 750.

Convert to delivered heat. 750 therms x 100,000 BTU x 0.80 = 60,000,000 BTU, or 60 million BTU delivered last season. This is the house's real seasonal heating need, as far as the gas bills can tell you.

Ask what other equipment would need to deliver the same 60 million BTU.

Run each back the other way: 7,034 x 8,530 = 60.0 million; 690 x 86,925 = 59.98 million; 516 x 116,340 = 60.03 million. Each closes within rounding.

What the customer gets: about 7,000 kWh a season with the heat pump against 750 therms today, plus the bill's rate per kWh and rate per therm to turn each into cost. What the customer does not get from you is a statement that one is cheaper, because that depends on their two rates, which the strip does not know.

What changes the answer.

• The old furnace was probably not delivering 80 percent. AFUE is a test result when new. Twenty years of oversizing, short cycling and a dirty heat exchanger may mean it delivered less. If it really ran at 72 percent, the house needed only 750 x 100,000 x 0.72 = 54 million BTU, and the heat pump would need 54,000,000 / 8,530 = 6,331 kWh. Give the customer that as a range rather than one number.
• The seasonal COP includes the backup strips. A heat pump that hands the coldest hours to resistance heat runs at COP 1.0 during those hours. In a cold climate the seasonal figure for the whole system is lower than the compressor's rating suggests, sometimes by a lot. See related: The Bill That Doubled From Emergency Heat.
• Ducts. Heat lost from ducts in an attic or crawlspace is lost whichever ducted system feeds them, so it cancels when comparing a ducted furnace with a ducted heat pump on the same ducts. It does not cancel against ductless equipment or baseboard.
• The gas furnace also used electricity. Its blower and inducer draw power that AFUE does not count, and the heat pump's kWh already include its own blower. A careful comparison adds the furnace's electricity to its side.
• Gas billed in ccf. If the bills were in ccf, convert with the therm factor before step one, or every figure above is off by that factor.

Where the comparison usually goes wrong

Comparing COP to AFUE directly. A COP of 2.5 and an AFUE of 95 are not "2.5 against 0.95, so the heat pump is two and a half times better". They apply to different units bought at different prices. Only the cost per million BTU delivered, built from both rates, says which costs less.

Using a rated COP for a cold-weather month. A rating at 47 F applied to January in a cold climate overstates the heat pump's output per kWh in exactly the month that dominates the season.

Comparing a gallon with a gallon. A customer switching from oil to propane hears both priced per gallon and assumes the gallons are equivalent. A gallon of oil carries 138,500 / 91,500 = 1.51 times the energy of a gallon of propane, so the same house burns roughly half again as many gallons of propane, less whatever the newer equipment's efficiency claws back. In the worked example, 690 gallons of propane against 516 of oil is 690 / 516 = 1.34 times as many gallons, because the propane furnace was modeled at 95 AFUE against the oil furnace's 84.

Using the whole gas bill as heating. Leaving the water heater and range in the heating therms inflates the house's heat need and makes every replacement look like it costs more to run.

References

• U.S. Energy Information Administration, published heat content of fuels
• U.S. Department of Energy, residential furnace and heat pump efficiency rating definitions (AFUE, HSPF, HSPF2)
• See related: What an Efficiency Number Actually Compares
• See related: What a BTU Actually Is
• See related: Savings Claims Without Overpromising: The Honest Language