Compare dollars per delivered heat
A dual-fuel system can use a heat pump or a furnace, but the cheapest source can change with utility rates and heat pump efficiency. The economic question is separate from whether the heat pump has enough capacity at a particular outdoor temperature.
Use electricity in dollars per kWh, natural gas in dollars per therm, furnace AFUE as a decimal, and heat pump COP for the operating condition. EIA identifies a therm as 100,000 Btu, while one kWh is approximately 3,412 Btu. Those conversions allow a common basis.
The equations
For one million Btu of useful heat, ignoring distribution losses and additional consumption not represented in the inputs:
Heat pump cost = (1,000,000 ÷ 3,412) × electricity price ÷ COP.
Gas furnace cost = 10 × gas price per therm ÷ AFUE.
Set the two equal and rearrange:
Break-even COP = (100,000 ÷ 3,412) × electricity price × AFUE ÷ gas price per therm.
Use 0.95 for a 95% AFUE furnace, not 95. COP is a ratio, not a percentage and not HSPF2. The PNNL pre-retrofit guide distinguishes fuel-utilization efficiency from heat-pump COP.
Worked example
Assume illustrative rates of $0.18/kWh and $1.50/therm, with furnace AFUE 0.95. The break-even COP is (100,000 ÷ 3,412) × 0.18 × 0.95 ÷ 1.50, or about 3.34.
| Heat pump COP | Heat pump cost per million Btu | Furnace cost per million Btu |
|---|---|---|
| 2.0 | $26.38 | $15.79 |
| 3.0 | $17.58 | $15.79 |
| 3.34 | About $15.79 | $15.79 |
| 4.0 | $13.19 | $15.79 |
Above the break-even COP, the heat pump has the lower modeled variable energy cost. Below it, the furnace does. The figures are arithmetic scenarios, not current national rates, quoted bills, or a recommendation for a particular thermostat setting.
Use the heat pump versus gas calculator to repeat the comparison with your assumptions. For a full installation decision, read heat pump versus furnace ownership costs.
Prepare the utility inputs carefully
Include variable supply and delivery charges. Exclude fixed charges that remain regardless of which heating source runs for an extra hour. If eliminating gas service would remove a fixed fee, evaluate that separately as part of a whole-project decision. It usually does not affect hourly dispatch in a dual-fuel system that retains the gas account.
If gas is billed in Ccf or Mcf, use the utility’s billed energy conversion to obtain a per-therm rate. Do not treat one Ccf as exactly one therm without checking the bill. For time-of-use electricity, repeat the equation for each relevant rate period. A single monthly average can conceal a costly peak window.
COP does not directly give an outdoor temperature
To translate break-even COP into a switching strategy, the installer needs the exact system’s performance at relevant temperatures and operating outputs. The same nominal model family may have different matched-system performance. A brochure maximum is not sufficient.
Capacity also constrains the decision. Even when heat pump energy is cheaper, it may need help if it cannot meet the load. Conversely, it can have enough capacity while gas is cheaper under the selected rates. The backup-heat guide explains this distinction.
Important limits of the simple model
The equations omit fixed fees, financing, maintenance, and any fan or standby energy not included in the input assumptions. Defrost, cycling, and distribution can affect delivered performance. Small modeled differences should be treated cautiously when input uncertainty is large.
Do not use the result to override safety controls or arbitrarily change installer lockouts. Ask a qualified contractor to commission the appropriate manufacturer-supported control sequence. Record the assumed rates so the economic comparison can be reviewed when tariffs change.
A useful break-even calculation identifies the conditions under which each source is favored. It does not establish a universal “switch to gas below 35°F” rule for every house and heat pump.