How to Compare Heating Costs Across Fuels per Million BTU

Why this matters

"Would a heat pump be cheaper to run than my gas furnace?" gets answered in most living rooms with a feeling, a brochure number or a neighbor's story, and any of those can be wrong in either direction. The shop that gives the wrong answer owns it when the first winter's bills arrive. The honest answer is one line of arithmetic run on the customer's own prices: what it costs to put one million BTU of heat into the house with each option. It takes ten minutes at the kitchen table, uses only the bills on the counter, and tells you not just which option is cheaper but by how much and at what price ratio the answer would flip.

The formula, and what each term means

Cost per million BTU delivered = price per unit x 1,000,000 / (BTU per unit x efficiency)

• Price per unit is what the customer pays for one more kWh, therm or gallon. Step 1 sets exactly which price.
• BTU per unit is the heat content of the fuel as bought. A million BTU is written MMBtu in most trade references.
• Efficiency is the share of that heat that ends up in the house. For a furnace or boiler it is AFUE, a fraction below 1. For a heat pump it is COP, heat delivered per unit of electric energy, which is above 1 in most weather. COP, AFUE and Delivered Heat: Putting Every Fuel on One Scale owns those definitions; this card only uses them.

The middle piece, 1,000,000 / (BTU per unit x efficiency), is the number of units it takes to deliver one MMBtu. Compute it separately, because it does not change when prices do. Work it once per piece of equipment and you can re-price the whole comparison in a minute every time a rate moves.

Units check: price per unit x BTU / (BTU per unit) leaves price, per MMBtu. If your units do not cancel to that, a term is wrong.

Step 1: Take the price of the next unit, from the customer's own bills

Find what the customer pays for one more unit of energy: the energy or commodity charge, plus every charge printed per kWh, per therm or per gallon (delivery, distribution, fuel adjustment, per-unit riders), plus the tax on those. Leave out the fixed monthly customer charge.

Why: a change of heating equipment changes how many units the house buys, not whether it keeps the account. The fixed charge is paid either way.

What breaks if you skip it: dividing the whole bill by the units on it gives the average price, and in a low-use month the fixed charge spread over few units can push that far above the price of the next unit. Run on summer averages, gas looks dearer than it is in January.

Two exceptions. If the switch would close the gas account entirely (no water heater, range or dryer left on gas), the fixed gas charge goes away, and that saving belongs in the comparison as a yearly amount added at the end, not folded into a per-unit price. And if the electric rate is tiered or seasonal, heating kWh land on top of everything else the house already uses, so they are priced at the top tier the winter bill reaches. See related: Tiered and Seasonal Rates: Why the Last Kilowatt-Hour Costs More.

For delivered fuels, use the price per gallon on the most recent tickets, and note whether it is a contract price or a will-call price, because they can differ.

Step 2: Write every fuel's price as a multiple of the kWh price

Divide each fuel's price per unit by the price of a kWh and carry the ratio instead of the currency. Call the kWh price E. On the worked house below, the bills put a therm of gas at 9 E, a gallon of propane at 18 E and a gallon of heating oil at 24 E. Those ratios are illustrative; use the ones your customer's bills produce.

Why: the ratio is what decides the comparison. Two houses on completely different rates with the same therm-to-kWh ratio get the same answer, and a ratio does not go stale the way a price does.

Step 3: Use the right heat content for each fuel

Gas billed in CCF (hundred cubic feet) must be converted to therms with the therm factor printed on the bill before the 100,000 applies. See related: Anatomy of a Natural Gas Bill and the Therm Conversion.

Step 4: Pick the efficiency that applies at this house

Furnace or boiler: the AFUE of the actual or proposed unit, from its rating plate or its certified rating listing. Enter a 95 percent unit as 0.95. An old unit's rating is its rating when new; if it is decades old, say so in the write-up rather than guessing a lower figure.

Electric resistance: 1.0. Every kWh becomes 3,412 BTU in the house.

Duct losses: leaky ducts in an attic or crawlspace lose heat whatever fuel feeds the air handler, so when both options use the same ducts, leave the losses out of both. When one option is ducted and the other is not (baseboard, ductless heads inside the conditioned space), the ducted option carries a loss the other does not, and the comparison has to say so even if it cannot put a number on it.

Heat pump: the term that decides most comparisons, and the one most often taken from the wrong place. It gets its own step.

Step 5: Take the heat pump's COP at the temperatures where the heat is delivered

A heat pump's COP falls as the outdoor temperature falls, and the house needs more heat as the outdoor temperature falls. So most of a season's heat is delivered in hours colder than average, at COPs below the headline. Heating ratings under AHRI 210/240 are published at fixed outdoor test points, 47 F and 17 F among them; the 47 F figure is the one that tends to reach the brochure, and it describes mild weather.

Split the season's heat into a few temperature bins, give each the COP the manufacturer's extended performance data shows at that temperature, and average the kWh, not the COP. For the worked house, from its load calculation and local bin weather:

• 30 percent of the season's heat at a COP of 3.5 (mild days)
• 50 percent at a COP of 2.6 (ordinary winter)
• 20 percent at a COP of 1.8 (cold snaps)

kWh per MMBtu in each bin is 1,000,000 / (3,412 x COP): 83.7, 112.7 and 162.8. Weighted by share of heat: 0.30 x 83.7 = 25.11, 0.50 x 112.7 = 56.35 and 0.20 x 162.8 = 32.56, which add to 114.0 kWh per MMBtu. Resistance takes 293.1 kWh for the same heat, so the effective seasonal COP is 293.1 / 114.0 = 2.57.

Averaging the COPs instead gives 0.30 x 3.5 + 0.50 x 2.6 + 0.20 x 1.8 = 2.71, which flatters the heat pump by about 5 percent (2.71 / 2.57 = 1.05). The cold bin's kWh count for more than its COP suggests, so the energy is what gets averaged.

If backup strips carry part of the cold bin, that share runs at a COP of 1.0 and goes into the weighting as its own line. How the lockout or the switchover to a furnace should be set is a separate decision; see related: Backup Heat: Dual Fuel or Resistance.

If you have no bin split, say the answer rests on an assumed one, and rerun it with a bigger cold bin to show the customer how much the conclusion depends on it.

Step 6: Fill in the worksheet

Compute units per MMBtu for each option, then multiply by its price ratio.

COST PER MILLION BTU DELIVERED
Price basis: E = the price of one kWh on the bill

OPTION        PRICE  BTU/UNIT  EFF    UNITS/MMBTU  COST
Heat pump     1 E    3,412     2.57   114.0 kWh    114.0 E
HP, 47 F only 1 E    3,412     3.5    83.7 kWh     83.7 E
Resistance    1 E    3,412     1.0    293.1 kWh    293.1 E
Gas furnace   9 E    100,000   0.95   10.526 thm   94.7 E
Propane furn  18 E   91,500    0.95   11.504 gal   207.1 E
Oil furnace   24 E   138,500   0.84   8.595 gal    206.3 E

Break-even therm price vs heat pump: 27.84 / COP x E
At COP 2.57: 10.8 E. This house pays 9 E.

The second row is not an option. It is the brochure number, printed so the customer can see what it would have claimed.

Reading the worksheet

Against gas, the heat pump loses at this house's prices. 114.0 E against 94.7 E per MMBtu: 114.0 / 94.7 = 1.20, so the heat pump costs about 20 percent more per unit of heat delivered. The brochure row would have said the opposite: 83.7 E is 1 minus 83.7 / 94.7, about 12 percent cheaper than gas. That gap between the two rows is the whole reason Step 5 exists.

Against propane and oil, it wins clearly. 114.0 / 207.1 = 0.55 and 114.0 / 206.3 = 0.55, so about 45 percent less per MMBtu than either. Resistance, at 293.1 E, is the ceiling for any electric option.

The break-even ratio is the most useful line on the sheet. The heat pump beats a 0.95 gas furnace when the therm price exceeds (100,000 x 0.95) / (3,412 x COP) times the kWh price, which is 27.84 / COP. At an effective COP of 2.57 that is 10.8. This customer pays 9, so gas wins today; if the therm rose to 11 E with electricity flat, the heat pump would edge ahead. Customers understand a ratio they can watch on their own bills.

Run the same line the other way and you get the switchover. At 9 E, the heat pump beats gas only in hours when its COP is above 27.84 / 9 = 3.09, which here is the mild bin alone. Running the heat pump in the mild bin and the furnace for the rest costs 0.30 x 83.7 + 0.70 x 94.7 = 25.1 + 66.3 = 91.4 E per MMBtu, about 3.5 percent under all-gas (91.4 / 94.7 = 0.965). Against propane the break-even COP is 86,925 / (3,412 x 18) = 1.42, so the heat pump stays cheaper even in this house's cold snaps at 1.8.

Turning it into a season. Last winter's bills show about 600 therms of heating gas (after removing the water heater and range share; How to Weather-Normalize Two Winters of Bills shows how) burned in an existing furnace rated 0.80. That is 600 x 100,000 x 0.80 = 48 MMBtu delivered. At 94.7 E a new gas furnace delivers it for 48 x 94.7 = 4,546 E; the heat pump for 48 x 114.0 = 5,472 E. The difference is 926 E, the price of about 926 kWh a season, in gas's favor. Present it as an estimate from last winter's weather and this year's prices, never as a promise. See related: Savings Claims Without Overpromising: The Honest Language.

What changes the answer

• A colder bin split. Move 10 points of heat from the ordinary bin into the cold bin and the weighted kWh rise from 114.0 to 119.0 (0.30 x 83.7 + 0.40 x 112.7 + 0.30 x 162.8), an effective COP of 2.46, and the break-even therm ratio climbs to 11.3.
• A time-of-use electric rate. Heating hours that fall in a peak window are priced at the peak rate, so E for heating is a weighted price over the hours the heat actually runs. See related: Time-of-Use Rates and Equipment Settings.
• The gas account closing. The yearly fixed charges come off the gas side of the ledger as a lump, which can matter more than the per-MMBtu gap on a mild-climate house that buys little heat.
• Ductwork that only one option uses, as in Step 4.

How to check your worksheet before you show it

• The resistance row must read 293.1 kWh. If it does not, the 3,412 is wrong somewhere.
• Reverse one row. 114.0 kWh x 3,412 x 2.57 should come back to about 1,000,000 BTU. It gives 999,600.
• A gas row near 10.0 therms means the efficiency was entered as 1. A 95 percent furnace needs a little over 10.5.
• The units column must not change when you change a price. If it did, a price leaked into the wrong column.
• Every COP on the sheet names its temperature. A COP with no temperature beside it is the brochure row in disguise.

References

• See related: COP, AFUE and Delivered Heat: Putting Every Fuel on One Scale
• See related: Backup Heat: Dual Fuel or Resistance
• See related: Savings Claims Without Overpromising: The Honest Language
• See related: Anatomy of a Natural Gas Bill and the Therm Conversion
• AHRI Standard 210/240, the rating standard for unitary air conditioners and air-source heat pumps, which sets the outdoor test temperatures behind published heating capacity and COP