Heat pump versus gas furnace: the annual saving

Where the operating-cost crossover actually sits

The engine prices the identical winter twice — once through the coefficient of performance at the electricity tariff, once through seasonal efficiency and calorific value at the gas price — and subtracts the heat-pump season from the gas season. Both sides consume the same delivered-heat figure, so the building cancels out of the verdict: what remains is machines and markets. A positive result says the compressor undercuts the burner; a negative one says it does not, and the pack declares a warning for that outcome so a negative saving reads as the reversal it is.

The quantity doing the real work is the RATIO of the two energy prices — what traders would call a spark spread between electricity and gas. The relation is linear in each price, so doubling both leaves the winner unchanged and merely scales the margin. Operating-cost parity — the crossover — sits where the electricity-to-gas price ratio equals what the machines themselves imply, the coefficient set against efficiency and energy content. A better compressor pushes the crossover toward dearer electricity; a condensing furnace drags it back.

The interesting output is therefore often not the difference but its distance from zero. A verdict that flips on a small tariff movement is a coin resting on its edge, and either energy market can tip it. The declared chart sweeps the tariff across its band and traces the saving through the crossover — the margin behind today’s answer, the sensitivity a single-scenario result hides.

The choice of heating also chooses an exposure: gas heating rides the gas market, an electrified house rides the power market with the coefficient as a cushion. The saving returned here is a snapshot of one year’s prices, and treating a snapshot as a forecast is the classic error in fuel-switching arithmetic — the honest use re-runs the verdict across the prices each market plausibly offers.

The declared reverse workflow solves for the tariff that produces a chosen saving — and a target of nothing at all makes it a break-even finder: the tariff at which the machines tie on this house, at this gas price, with these ratings. The gap between that parity tariff and the one on the bill states how far the local market sits from the crossover.

When this calculation is used

• Testing a fuel-switching proposition against local prices: the same winter priced both ways, verdict and margin on one screen.
• Stress-testing a verdict — sweeping the tariff through its band, or re-running with next winter’s contracted gas price, to see whether the sign survives.
• Finding the parity point: the declared reverse workflow solves for the tariff at which the machines tie, the number to compare a bill against.

Worked example

Run the pack’s declared anchor contest: the cluster’s reference winter, a typical heat pump against a condensing furnace, at mid-range electricity and gas prices under the utility’s declared calorific value.

The engine returns both annual costs and their signed difference — and at the anchor’s prices the difference comes back negative, the declared warning firing to say the heat pump LOSES this contest. That is the page working as intended: the anchor shows the sign doing its job, and how close to parity an ordinary market can sit.

Every figure in this example is produced by the certified engine when the calculator loads, checked against the signed pack’s declared test vectors; nothing on this page stores an answer. Then let the declared chart sweep the tariff: where the traced saving crosses zero is the parity tariff, and its distance from the anchor’s tariff is the whole story of this verdict.

What each input represents

Assumptions and limits

• Both machines serve the identical delivered-heat load, so dual-fuel arrangements — a compressor carrying mild weather, the burner covering cold snaps — fall outside this all-or-nothing comparison.
• Prices are single flat rates on each side; time-of-use electricity, tiered gas blocks and seasonal contracts must be blended before entry.
• The comparison is operating cost only: purchase, installation, venting, electrical work and equipment lifespan belong to the payback siblings in this pack.
• The snapshot prices are treated as the year’s prices. A verdict near parity is fragile by construction, and the sweep chart, not the single answer, is the honest reading there.

What the guards protect against

• The calorific value is held to the band real pipeline gas occupies, and the pack ships the refusal below that band as a declared test vector — an energy content quoted in another unit system would silently tilt the contest.
• The coefficient of performance may not fall below unity: below it, the machine would trail even a resistance element, and the contest would no longer involve a heat pump.
• Furnace efficiency must be positive and may not exceed unity, refusing both the division-destroying zero and the undivided percentage — beyond unity the contest would be lost by physics rather than by prices.

Provenance

Heating-fuel cost-comparison method: each fuel’s cost of delivered heat as its price over its efficiency, compared on an identical load

The same annual delivered heat is priced through the heat pump’s seasonal coefficient at the electricity tariff and through the furnace’s seasonal efficiency and calorific value at the gas price, and the difference is returned with its sign; the declared reverse workflow solves for the tariff that yields a chosen saving, and the declared chart sweeps the tariff across its band.

Screening and reference material, to be checked against the governing standard and a qualified engineer; not a design determination. The signed pack carries its own citation, which displays from the verified leaf when the calculator loads.