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.

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

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: 632 therms × $1.50 = $948/year

Now gas wins by over $1,000.
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 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 — running it for a few weeks in January can wreck the annual cost calculation.
And the federal IRA heat pump tax credit (30%, up to $2,000) plus utility rebates (often $1,500-3,000) cut the upfront cost difference enough that even a 5-year payback is realistic in many regions.

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.