Methodology

Every constant, every source, and the conditions under which this model would be wrong.

By Ash Banerjee, B.Tech, Mechanical Engineering. Published .

This site models operating cost only: what it costs to deliver heat, given your fuel prices and your equipment. It does not model purchase price, installation, financing, rebates, emissions, or comfort. Those matter. They are not what this calculator answers.

This page is the arithmetic. If you want the answer rather than the working, the calculator takes your own rates, the state pages apply these constants to every state, and the running cost guide explains what the output means. If you want to test the model against reality rather than against itself, the household dataset is real reported consumption from people who published their numbers.

The one equation

A heat pump costs less to run than a combustion furnace when:

electricity $/kWh ÷ fuel $/kWh-equivalent  <  effective COP ÷ AFUE

The left side is your local fuel price ratio. The right side is set entirely by your equipment. There is no universal threshold, which is the single most common error in published comparisons.

Both halves are worked through elsewhere. The gas furnace comparison derives the right hand side from first principles and validates it two ways. The note on the 3.5 to 1 rule explains why the number people quote is a special case of this equation rather than a law, and the glossary defines every term in it.

Constants

ConstantValueNote
BTU per kWh3,412.14International table BTU
BTU per therm100,000Exact by definition
Natural gas heat content1,037 BTU/cfEIA convention. Delivered gas runs roughly 1,020 to 1,050
Propane heat content91,500 BTU/galStandard figure for HD-5 propane
No. 2 heating oil heat content138,500 BTU/galStandard figure

The four assumptions

  1. Natural gas carries 1,037 BTU per cubic foot. Real delivered gas varies by utility and season.
  2. HSPF2 divided by 3.41214 gives seasonal COP. HSPF2 is measured under AHRI 210/240-2023 in one climate region, so your actual seasonal COP will differ with climate.
  3. Electric resistance backup runs at COP 1.0, weighted harmonically by share of heat delivered rather than by runtime.
  4. No winner is declared inside a 10% margin. Fuel prices move more than that between seasons.

Assumption three is the shakiest and the most consequential. Backup heat fraction depends on the balance point of a specific installation, which a state level model cannot know. It is exposed as an input rather than guessed.

Why the 3.5 to 1 rule is not a law

A ratio of 3.5 is what the equation returns for one specific pairing. Change either machine and the threshold moves a long way.

PairingBreakeven ratio
HSPF2 11.0 against 95% AFUE3.39
HSPF2 8.0 against 95% AFUE2.47
HSPF2 11.0 against 80% AFUE4.03
HSPF2 11.0 against 95% AFUE with 15% backup heat2.54

A single realistic backup heat assumption moves the threshold by 25%.

Data sources

Why the heating season, and not the latest month

EIA's residential price is revenue divided by volume. In summer, residential gas volume approaches zero while the fixed monthly customer charge remains, so the apparent price per unit roughly doubles. Using a summer month to answer a winter question overstates the cost of gas and biases the comparison toward the heat pump.

Both fuels are therefore averaged over the most recent complete December to February window, currently 2025-12, 2026-01, 2026-02, using identical months for every state. States without complete season data are excluded rather than estimated.

What would change our answer

Known limitations

Where this model gets tested

An equation that is only ever checked against itself is not worth much. Three things on this site test these constants against something external, and all three are worth reading before trusting the output above.

A commissioned Manual J load calculation put the heat loss coefficient of a real 2,000 sq ft house at 7.75 BTU per square foot per heating degree day, against the 8 this model uses as its default. The household dataset normalises real reported consumption onto one scale and finds households with no identified fault sitting in a narrow band, which is what you would expect if the normalisation is sound and not what you would see if it were meaningless. And the corrections log records the three occasions this model has produced an answer that turned out to be wrong, including one where a wrong price window flipped the verdict in fifteen states.

If you find a fourth, it is worth sending, and the standard this site holds itself to on errors is that they get published rather than quietly edited.