The 3.5 to 1 rule describes two specific machines
Derive the threshold rather than quoting it and you find it moves by more than 60% across ordinary equipment.
By Ash Banerjee. Published 2026-08-31.
A number circulates in heat pump discussion: if the price of electricity divided by the price of an equivalent amount of gas is below about 3.5 to 1, the heat pump wins on running cost. Above about 5 to 1, the furnace wins.
The number is not wrong. It is incomplete in a way that matters, because it is the answer for one pairing of machines and it is usually quoted as though it applied to all of them.
Deriving it
Take a house that needs a fixed amount of useful heat over a season, call it Q.
A gas furnace with efficiency AFUE burns Q divided by AFUE worth of fuel. At a fuel price of P dollars per unit of chemical energy, that costs Q times P divided by AFUE.
A heat pump with seasonal coefficient of performance COP consumes Q divided by COP in electricity. At E dollars per kWh, that costs Q times E divided by COP.
The heat pump is cheaper when the second is smaller than the first. Q cancels, and rearranging gives:
The left side is a property of your utility bills. The right side is a property of your equipment, and nothing else. There is no climate term, no house size term, and no national constant. The threshold is the ratio of the two machines' efficiencies.
Where 3.5 comes from
HSPF2 is the heating seasonal performance factor under AHRI 210/240-2023, measured in BTU of heat delivered per watt hour of electricity. Dividing by 3.41214 converts it to a dimensionless COP. An HSPF2 of 11.0, which is a good cold climate unit, gives a COP of 3.22.
Against a 95% AFUE condensing furnace, the threshold is 3.22 divided by 0.95, which is 3.39. Round it and you have the number everyone repeats.
So the rule of thumb quietly assumes a high performing heat pump against a high efficiency furnace, with no backup heat at all. Change any of those and the threshold moves.
| Heat pump | Furnace | Backup heat | Breakeven ratio |
|---|---|---|---|
| HSPF2 11.0 | 95% AFUE | none | 3.39 |
| HSPF2 8.0 | 95% AFUE | none | 2.47 |
| HSPF2 11.0 | 80% AFUE | none | 4.03 |
| HSPF2 11.0 | 95% AFUE | 15% | 2.54 |
| HSPF2 8.0 | 95% AFUE | 15% | 2.07 |
From 2.07 to 4.03 is a spread of 95%. A homeowner in a state with a price ratio of 3.0 gets opposite answers depending on which pair of machines is in the comparison, and the rule of thumb gives them no way to tell which case they are in.
Why it matters more than it looks
The two extreme rows are not exotic. A builder grade heat pump at HSPF2 8.0 is what goes into a lot of new construction on a cost bid. An 80% AFUE furnace is what sits in millions of older homes that never had a condensing unit installed. Realistic backup heat fractions in cold climates run well above 15% when a system is undersized.
Someone replacing an 80% furnace with a good cold climate heat pump has a threshold near 4.03 and will do well in most of the country. Someone replacing a modern 95% furnace with a builder grade unit that leans on resistance backup has a threshold near 2.07 and will lose money in most of the country. Both of them read the same 3.5 rule.
The useful version of the rule
If you want one number to carry around, carry the equation instead. Divide your heat pump's HSPF2 by 3.41 to get its COP, adjust it down for whatever share of heat you expect the backup strips to carry, and divide by your furnace's AFUE. That is your threshold. Then compare it against your own two utility bills.
Everything else is somebody else's equipment.
How this was checked
I derived the threshold rather than quoting it. Setting the running cost of a furnace equal to the running cost of a heat pump for the same delivered heat, then rearranging, gives a breakeven that depends only on effective COP divided by AFUE.
I checked that two ways. Working in dollars per unit of chemical energy and working in dollars per delivered BTU produce the same threshold, which they should. And the figure the derivation returns for an HSPF2 11.0 unit against a 95% AFUE furnace is 3.39, close enough to the 3.5 that circulates in the trade press that I am confident the rule of thumb is describing that specific pairing.
Every row in the breakeven table is computed by the same function the calculator uses, so the article and the tool cannot disagree.
References
- Air-Conditioning, Heating, and Refrigeration Institute. AHRI Standard 210/240-2023: Performance Rating of Unitary Air-Conditioning and Air-Source Heat Pump Equipment. This standard defines the M1 test procedure and the HSPF2 metric.
- U.S. Energy Information Administration. Units and calculators explained, energy conversion factors and fuel heat content.
- U.S. Federal Trade Commission. Appliance Labeling Rule, 16 CFR Part 305, which governs AFUE disclosure on heating equipment.