Heat pump versus resistance: the annual saving

What the compressor’s multiple is worth against the element

The relation prices the same winter twice and subtracts. The resistance side is the reference bill — load times tariff, one-for-one. The heat-pump side divides the load by the seasonal coefficient before the tariff touches it, because the compressor moves most of its warmth out of the outdoor air rather than making it. With load and tariff shared, the difference collapses to the resistance bill scaled by the share of heat the machine moves rather than makes — the coefficient, read directly as money.

This page completes a pair. The heat-pump-versus-gas comparison crosses energy markets — two fuels, two prices, two efficiencies, and a verdict that swings with the ratio between markets. This one never leaves the electricity meter, so no fuel price movement can touch the verdict: whatever the tariff does, the compressor undercuts the element in the same proportion. For an all-electric house the question is not whether the heat pump wins but by how much.

The reciprocal in the relation carries a lesson about diminishing returns. Moving from the element to a modest compressor deletes most of the bill; moving from a modest compressor to an excellent one deletes a thinning slice of what remains, because each step up the coefficient shrinks a bill already shrunk. Most of the prize is captured by getting off resistance at all — a reason to distrust premium-model arithmetic that prices the last step as if it were the first.

The coefficient that belongs here is the seasonal average, not the brochure rating: the winter-long figure that survives cold-snap derating, defrost cycles and any backup-strip hours — hours which, by running the element this page is comparing against, drag the machine back toward parity exactly when the load peaks. The heat-pump cost page carries the full account of that humility.

The declared reverse workflow inverts the economics: fix the annual saving the switch must earn — an instalment to cover, a payback target to meet — and the engine solves for the electricity price at which it does. Read against the bill, that parity tariff says whether the local market already pays for the machine or whether the case leans on electricity getting dearer.

When this calculation is used

• Pricing the switch for an all-electric house — baseboards, strips or a plug-in-heater winter — before a heat-pump quote is signed.
• Reading alongside the versus-gas page: a household weighing electrification from either starting fuel sees which comparison its own furnace room actually poses.
• Feeding the retrofit payback sibling: this annual saving is the denominator the installed cost is divided by.
• Solving backwards — the declared reverse workflow — for the tariff at which the switch earns a chosen annual figure.

Worked example

Run the pack’s declared reference switch: a family home’s ordinary season of delivered heat, priced once through bare resistance and once through a heat pump at a typical seasonal coefficient, both billed at the same mid-range residential tariff.

The engine returns the annual saving and, behind it, each machine’s full-season cost. Read the two costs before the difference: the resistance figure is the ceiling this pack prices every electric winter against, and the gap down to the compressor’s figure is the coefficient made visible in money.

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. Step the coefficient upward and watch the saving grow by thinning increments — the reciprocal at work, and the reason the first step off resistance is worth more than every refinement after it.

What each input represents

Assumptions and limits

• Both machines serve the identical heat load: comfort delivered is unchanged by the switch, and any rebound — heating rooms the baseboards left cold — sits outside the relation.
• One season-average coefficient stands in for the whole winter; backup-strip recoveries and cold-climate derating are presumed already folded into it.
• One flat tariff prices both winters; a time-of-use plan that treats a compressor’s hours differently from a baseboard’s must be blended before entry.
• This is an operating comparison only. Purchase, installation and switchboard work belong to the payback calculators this pack carries as siblings.

What the guards protect against

• A coefficient below unity is refused — the pack ships the refusal as a declared test vector — because a machine that delivers less warmth than it draws is worse than the element it is meant to beat, and the comparison’s premise would be inverted rather than answered.
• The coefficient is also capped well above anything a residential machine achieves, so a percentage entered where a ratio belongs is refused rather than silently pricing an impossible saving.
• The heat load must be positive and is bounded far above any dwelling’s demand, and the tariff band refuses prices quoted in cents entered as dollars — mistyped units, not markets.

Provenance

Heating-fuel cost-comparison method: cost of delivered heat as fuel price over efficiency, compared across two electric heating systems on one tariff

The annual heat load times the tariff prices the resistance winter; the load divided by the seasonal coefficient and priced at the same tariff gives the heat pump’s winter; their difference is the annual saving, and the declared reverse workflow solves for the tariff at which the saving reaches a chosen figure.

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.