Heat Pump vs Furnace: 15-Year Cost Calculator 2026

How heat pump vs furnace cost is worked out

A heat pump and a furnace are priced on the same annual heating load, so efficiency is the only energy difference. The heat pump’s electricity is the load divided by 3,412 (the BTU in a kilowatt-hour) divided by the COP, in kilowatt-hours, and the energy cost is the kilowatt-hours times the price a kWh. The furnace’s gas is the load divided by the AFUE as a decimal divided by 100,000 (the BTU in a therm), in therms, and the energy cost is the therms times the price a therm. The total is the install cost plus the years times the energy cost plus the maintenance: $150 a year for the heat pump, $100 a year for the furnace. The winner is the smaller total.

At the defaults — 60,000,000 BTU a year, $0.17 a kWh, $1.50 a therm, heat pump install $12,000, furnace install $5,625, COP 3.0, AFUE 80%, horizon 15 years — the heat pump uses 60,000,000 ÷ 3,412 ÷ 3.0 = 5,861.66 kWh a year, which costs 5,861.66 × $0.17 = $996.48, for a total of $12,000 + $14,947.25 of energy + $2,250 of maintenance = $29,197.25. The furnace uses 60,000,000 ÷ 0.80 ÷ 100,000 = 750.00 therms a year, which costs 750.00 × $1.50 = $1,125.00, for a total of $5,625 + 15 × $1,125.00 + 15 × $100 = $24,000.00. The furnace wins by $29,197.25 − $24,000.00 = $5,197.25. A year costs $1,946.48 for the heat pump against $1,600.00 for the furnace.

The worked example, line by line

Setup: 60,000,000 BTU a year, $0.17 a kWh, $1.50 a therm, heat pump install $12,000, furnace install $5,625, COP 3.0, AFUE 80%, 15 years.

Line 1 — the heat pump energy. 60,000,000 ÷ 3,412 ÷ 3.0 = 5,861.66 kWh a year, and 5,861.66 × $0.17 = $996.48 a year.

Line 2 — the furnace energy. 60,000,000 ÷ 0.80 ÷ 100,000 = 750.00 therms a year, and 750.00 × $1.50 = $1,125.00 a year.

Line 3 — the heat pump total. $12,000 install + $14,947.25 of energy over 15 years + $2,250 of maintenance = $29,197.25.

Line 4 — the furnace total. $5,625 install + $16,875.00 of energy over 15 years + $1,500 of maintenance = $24,000.00.

Line 5 — the winner. $29,197.25 − $24,000.00 = $5,197.25 to the furnace. A year costs $1,946.48 for the heat pump against $1,600.00 for the furnace.

Every branch, checked

40M BTU/yr load: the heat pump uses 40,000,000 ÷ 3,412 ÷ 3.0 = 3,907.78 kWh a year, which costs $664.32, and the furnace uses 40,000,000 ÷ 0.80 ÷ 100,000 = 500.00 therms a year, which costs $750.00, for totals of $24,214.83 against $18,375.00. The furnace wins by $5,839.83. A smaller load grows the furnace’s lead, because the install gap matters more when the energy bills are small.

90M BTU/yr load: the heat pump uses 8,792.50 kWh a year, which costs $1,494.72, and the furnace uses 1,125.00 therms a year, which costs $1,687.50, for totals of $36,670.87 against $32,437.50. The furnace wins by $4,233.37. A bigger load narrows the gap, because the heat pump’s cheaper energy has more to work on — but at 90M BTU a year it is still not enough.

$0.10 a kWh (flip): the heat pump’s energy is 5,861.66 × $0.10 = $586.17 a year, for a total of $12,000 + $8,792.50 of energy + $2,250 of maintenance = $23,042.50, while the furnace stays $24,000.00. The heat pump wins by $957.50. Cheap electricity flips it, because the heat pump’s energy is the only thing that changes, and $410.32 a year for 15 years is $6,154.74.

$0.30 a kWh: the heat pump’s energy is 5,861.66 × $0.30 = $1,758.50 a year, for a total of $40,627.49, while the furnace stays $24,000.00. The furnace wins by $16,627.49. Dear electricity punishes the heat pump, because the heat pump’s whole bill is electricity.

$1.00 a therm: the furnace’s energy is 750.00 × $1.00 = $750.00 a year, for a total of $5,625 + 15 × $750.00 + $1,500 = $18,375.00, while the heat pump stays $29,197.25. The furnace wins by $10,822.25. Cheap gas is the furnace’s best case: its energy bill falls by a third, and the heat pump cannot follow.

$2.50 a therm (flip 2): the furnace’s energy is 750.00 × $2.50 = $1,875.00 a year, for a total of $5,625 + 15 × $1,875.00 + $1,500 = $35,250.00, while the heat pump stays $29,197.25. The heat pump wins by $6,052.75. Dear gas flips it the other way, because the furnace’s energy bill is now $878.52 a year more than the heat pump’s.

Heat pump install $8,000: the heat pump is $8,000 + $14,947.25 + $2,250 = $25,197.25, while the furnace stays $24,000.00. The furnace wins by $1,197.25. A $4,000 cheaper heat pump nearly closes the gap — the install is most of what the heat pump costs — but the energy and maintenance still leave the furnace ahead.

Furnace install $8,000: the furnace is $8,000 + $16,875.00 + $1,500 = $26,375.00, while the heat pump stays $29,197.25. The furnace wins by $2,822.25. A dearer furnace narrows the gap a lot, because the furnace’s install is most of its total, but $2,375.00 of extra install is still less than the $5,197.25 it was winning by.

COP 4.0: the heat pump uses 60,000,000 ÷ 3,412 ÷ 4.0 = 4,396.25 kWh a year, which costs $747.36, for a total of $12,000 + $11,210.43 of energy + $2,250 of maintenance = $25,460.43, while the furnace stays $24,000.00. The furnace wins by $1,460.43. A much better COP saves $249.12 a year, which is $3,736.79 over 15 years — nearly enough, but not quite.

AFUE 95%: the furnace uses 60,000,000 ÷ 0.95 ÷ 100,000 = 631.58 therms a year, which costs $947.37, for a total of $5,625 + $14,210.53 of energy + $1,500 of maintenance = $21,335.53, while the heat pump stays $29,197.25. The furnace wins by $7,861.72. A high-efficiency furnace widens the lead, because it burns 118.42 fewer therms a year for the same heat.

25-year horizon: the heat pump is $12,000 + $24,912.08 of energy + $3,750 of maintenance = $40,662.08, and the furnace is $5,625 + 25 × $1,125.00 + 25 × $100 = $36,250.00. The furnace wins by $4,412.08. A longer horizon narrows the gap, because the heat pump’s cheaper energy has more years to work — but 10 extra years only close $785.17 of it.

10-year horizon: the heat pump is $12,000 + $9,964.83 of energy + $1,500 of maintenance = $23,464.83, and the furnace is $5,625 + 10 × $1,125.00 + 10 × $100 = $17,875.00. The furnace wins by $5,589.83. A shorter horizon widens the gap, because the install gap is spread over fewer years of energy saving.

Flip-fail — $0.10 a kWh AND a 40M BTU/yr load: cheap electricity alone flips it, but a small load takes it back. The heat pump uses 3,907.78 kWh a year at $0.10, which costs $390.78, for a total of $12,000 + $5,861.66 of energy + $2,250 of maintenance = $20,111.66, while the furnace is $5,625 + 15 × $750.00 + $1,500 = $18,375.00. The furnace still wins by $1,736.66. One good condition is not enough when the other one works against it.

Reverse — the break-evens: electricity breaks even at about $0.11 a kWh (exactly $0.1109 a kWh): below that price the heat pump wins, above it the furnace wins. Gas breaks even at about $1.96 a therm (exactly $1.9620 a therm): above that price the heat pump wins, below it the furnace wins. The heat pump install breaks even at $6,802.75: at that install price the two totals tie at $24,000.00. COP breaks even at 4.60 (exactly 4.5992): a heat pump that efficient ties the furnace on these prices. The heating load breaks even at 221,760,547 BTU/yr (221.76M BTU/yr): above that load the heat pump wins, because its per-BTU cost is lower — but that is a very large home, far above the 60,000,000 BTU/yr default.

What the defaults assume

The model assumes both sides heat the same 60,000,000 BTU a year for the same 15 years, so efficiency is the only energy difference, and it assumes the electricity and gas prices stay flat for the whole horizon, with no price rises. It assumes COP 3.0 is the heat pump’s average efficiency across the whole heating season, which is a simplification: a real heat pump’s COP falls on the coldest days, when the load is highest, and it may need backup resistance heat. It assumes maintenance of $150 a year for the heat pump and $100 a year for the furnace, and it leaves out the ductwork, the cooling the heat pump also provides, the noise, the look of the outdoor unit, and the effect on the home’s value, which are real but not priced here. Rounding convention: money is rounded to cents, energy to 2 decimals, and all figures are computed from unrounded values, rounded only for display.

Output · formula · meaning

Who uses this

• The homeowner replacing a dead furnace: they learn a furnace costs $24,000.00 over 15 years against $29,197.25 for a heat pump — so they know the furnace saves $5,197.25, and they check the $0.10 a kWh case at $23,042.50 before they decide.
• The homeowner with cheap electricity: they learn the heat pump wins by $957.50 at $0.10 a kWh — so they know cheap electricity flips it, and they check the $0.11 a kWh break-even before they pay for the install.
• The homeowner in a big, cold house: they learn the heat pump wins above 221,760,547 BTU/yr of load — so they know a big load favours the heat pump, and they check the 90M BTU/yr case at $36,670.87 before they assume it wins at their size.
• The homeowner weighing a high-efficiency furnace: they learn a 95% AFUE furnace costs $21,335.53 over 15 years — so they know the dearer furnace widens the lead to $7,861.72, and they check the COP 4.0 case at $25,460.43 before they buy the heat pump.

Accuracy & limitations

The math is exact for the numbers you enter: the heat pump’s energy is the load divided by 3,412 divided by the COP, the furnace’s energy is the load divided by the AFUE divided by 100,000, the totals are the install plus the years times the energy plus the maintenance, and the winner is the smaller total. What the model cannot do is read your bills for you: check the electricity and gas prices on the bill, because a $0.10 bill and a $0.30 bill give opposite answers. It assumes the same load and the same horizon for both sides, flat prices, and a single COP for the whole season, and it leaves out the ductwork, the cooling the heat pump also provides, the noise, the look of the outdoor unit, and the effect on the home’s value. For sizing the furnace itself, see furnace size calculator; for sizing a boiler, see boiler size calculator.