Heat Pump vs Furnace Annual Heating Cost

Heat pumps deliver more heat than the electricity they consume because they move heat from outside instead of generating it.
A typical air-source heat pump produces 2-3.5 units of heat per unit of electricity, depending on outdoor temperature.
That number is called COP (Coefficient of Performance), and it is the only thing that makes electric heating cheaper than burning gas.

Heat is measured here in BTU (British Thermal Units). One BTU is the energy needed to raise one pound of water by one degree Fahrenheit, and a typical house needs 40 to 80 million of them over a heating season. Furnace efficiency is quoted as AFUE (Annual Fuel Utilization Efficiency), the fraction of the fuel’s energy that actually ends up in the house rather than going up the flue.

The math for heat pump:

annual_kWh = annual_BTU / (COP × 3,412) annual_cost = annual_kWh × electricity_price

The math for gas furnace:

annual_therms = annual_BTU / (AFUE × 100,000) annual_cost = annual_therms × gas_price

The 3,412 is the number of BTU in a kilowatt-hour. The 100,000 is the number of BTU in a therm, the unit gas is billed in.

A worked example.
1,800 sq ft Seattle home needing 60 million BTU/year of heat.
Heat pump at COP 3.0 (Seattle has mild winters): 60M / (3.0 × 3,412) = 5,860 kWh/year.
At $0.13/kWh: $762/year.

Same home with 95% AFUE gas furnace at $1.30/therm: 60M / 95,000 = 632 therms.
Cost: 632 × $1.30 = $821/year.

Heat pump wins by $59 in this case.
Move the same setup to Boston with $1.50/therm gas, $0.27/kWh electricity, and a heat pump COP of 2.4 (colder climate hurts COP):

• Heat pump: 60M / (2.4 × 3,412) = 7,326 kWh × $0.27 = $1,978/year
• Gas furnace: 631.6 therms × $1.50 = $947/year

Now gas wins by $1,031.
This is why the heat-pump-vs-gas debate is regional.
Mild climates with cheap electricity and expensive gas (West Coast) favor heat pumps.
Cold climates with expensive electricity (Northeast) often still favor gas, despite the marketing.

Cold-climate heat pumps change the math.
Hyper-heat units from Mitsubishi, Fujitsu, and Daikin maintain COP near 2.0-2.5 even at 0°F outside, where standard heat pumps drop to 1.5 or below.
A cold-climate heat pump in Boston might hit COP 2.7 average over the season instead of 2.0, which closes most of the cost gap with gas.
Same calculation with COP 2.7: 60M / (2.7 × 3,412) = 6,512 kWh × $0.27 = $1,758/year, still more than gas but the gap is a lot smaller.

Three details people miss.
The COP rating on the manufacturer label is at 47°F outside; real-world average COP across a heating season in cold climates is usually 2.0-2.5, not the rated 3.5-4.5.
Backup electric resistance heat (the “emergency heat” mode) drops COP to 1.0, and running it for a few weeks in January can wreck the annual cost calculation.
And incentives move the upfront comparison more than the fuel prices move the running comparison, but they change from year to year and the federal residential efficiency credit was cut back after 2025. Check what is actually live in your state and with your own utility before you count on any of it. Utility rebates in particular are often the larger number and get overlooked.

The right comparison is not really fuel cost.
Replacement cost is comparable: a new high-efficiency furnace plus AC is $8,000-12,000 installed; a cold-climate heat pump that handles both is $9,000-14,000.
The decision is more about future proofing. Gas prices have been volatile, electricity prices are stable to falling in most regions, and many cities are passing gas connection bans for new construction.