Heat pump annual heating cost

Why a heat pump is priced on heat moved, not heat made

The relation runs the way the physics does. The home demands a season of delivered heat — a quantity that belongs to the building, not to any appliance. Dividing that demand by the seasonal coefficient of performance yields the electricity the compressor must draw, and the tariff turns electricity into money. The division is the step a resistance heater never gets: a resistance element converts each unit of electricity into exactly one unit of warmth, while a vapour-compression machine uses the refrigerant cycle to deliver a multiple of what it consumes.

The coefficient that matters is the SEASONAL one, a smaller and humbler number than the rating a brochure leads with. Laboratory ratings are taken in mild air; a real winter drags the average down through cold-climate derating — the colder the source air, the harder the cycle works per unit moved — through defrost cycles that periodically run the machine backwards to clear the outdoor coil, and through any hours where backup resistance strips carry the load at parity. The input documented here is the season-long average that survives all of that, which is why an honest seasonal figure and an optimistic nameplate can price the same winter very differently.

Keeping the heat load separate from the machine is what makes this page comparable with its siblings. The delivered-heat figure is appliance-independent: the same quantity feeds the furnace page unchanged, because the building does not care what warms it. That separation lets the electrification question — what happens to this bill when a furnace gives way to a compressor — be asked with everything held equal except the machine, which is exactly what the comparison page then does.

The tariff carries its own subtlety. Heating through a heat pump ties the warmth of the house to the price of electricity, so what belongs here is the marginal per-unit price the extra winter consumption will be billed at, blended across the time-of-use windows a compressor actually runs through — and it runs the coldest nights hardest. A household moving from fuel to electricity is moving its exposure between energy markets, and this input is where that exposure enters the arithmetic.

The pack declares a reverse workflow that answers the budgeting question the forward one cannot: fix the annual amount to be spent on warmth and let the engine solve for the delivered heat that spending covers at the stated coefficient and tariff. Set against the load the house demands, the gap is the shortfall — or the headroom — the budget implies.

When this calculation is used

• Pricing a proposed heat-pump installation’s season before it exists, from an audited or bill-derived heat load and the unit’s rated seasonal coefficient.
• Re-pricing an existing heat pump’s winter after a tariff change, holding the building and the machine constant while only the price moves.
• Feeding the comparison: this cost is one side of the heat-pump-versus-gas saving this cluster computes on its own page.
• Solving backwards — the declared reverse workflow — from an annual heating budget to the delivered heat it buys.

Worked example

Run the pack’s declared reference season: a family home whose winter demands an ordinary quantity of delivered heat, served by a heat pump at a typical seasonal coefficient of performance and billed at a mid-range residential tariff — the same house the furnace and comparison pages price by other means.

The engine returns the annual heating cost and, separately, the electricity the compressor consumed to earn it. Read the distance between heat delivered and electricity drawn first: that gap is the warmth the machine moved rather than made, and the entire reason the bill undercuts a resistance heater’s for the same house.

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. Nudge the seasonal coefficient downward, as a harsher winter would, and the cost climbs in exact proportion — the sensitivity that makes the seasonal-versus-nameplate distinction worth money.

What each input represents

Assumptions and limits

• One season-average coefficient stands in for the whole winter: the swing between mild-day efficiency and cold-snap derating is already averaged into the single input.
• The heat load is taken as known and appliance-independent; estimating it belongs to the audit, the bills or the degree-day siblings in this pack.
• One flat tariff prices every unit; time-of-use windows, demand charges and seasonal rates must be blended into it beforehand.
• This is an operating cost only. Purchase, installation and maintenance sit outside the relation, in the payback calculators this pack carries as siblings.

What the guards protect against

• The coefficient of performance may not fall below unity, and the pack ships the refusal as a declared test vector. A machine below unity would deliver less warmth than the electricity it consumes — worse than a bare resistance element — which describes a broken machine or a mistyped input, not a heat pump.
• The coefficient is also capped well above anything a residential machine achieves, so a percentage entered where a ratio belongs — a hundredfold slip — is refused rather than silently pricing an impossible winter.
• The heat load must be positive and is bounded far above any dwelling’s demand, catching a lifetime total or watt-hours entered where kilowatt-hours belong.

Provenance

Heating-fuel cost-comparison method: cost of delivered heat as fuel price over efficiency, with the heat pump’s efficiency read as its coefficient of performance

Annual delivered heat is divided by the seasonal coefficient of performance to yield the electricity consumed, which the tariff prices into an annual cost; the declared reverse workflow solves the same relation for the heat load a stated budget covers.

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.