Heat-pump water heater annual cost

Why this coefficient lives in the room, not the weather

The relation runs the load through the machine before it reaches the money. Dividing the year’s delivered heat by the coefficient of performance yields the electricity the unit actually meters; the tariff prices only that. The division is the step the resistance benchmark never gets: most of the heat entering the water was gathered from the surrounding air, and the meter charged only for the gathering.

Its space-heating sibling wrestles the weather — that coefficient falls with the outdoor air it must draw on. A water heater’s coefficient lives somewhere gentler: the room around the tank. A basement or utility room holds a mild temperature all year, so the machine largely escapes cold-climate derating; what moves its coefficient instead is that room’s warmth, the setpoint the water must reach, and the shape of demand — a household draining the tank in one evening burst pushes the unit onto its backup resistance element, hours billed at the floor rather than the rating.

The honest input is therefore the whole-unit, uniform-energy-factor-type figure: an average over a standardised year of draws that already folds in standby losses and backup-element hours, which is why it sits well below the compressor’s flattering moment-to-moment best. Enter the rating the label declares for the unit’s draw class, and expect a cool room or a punishing draw pattern to shave it further.

The gathered heat is not conjured from nowhere. A tank standing inside the heated envelope pulls some of it, in winter, from the space-heating system — a quiet transfer between two bills that this relation does not price — while in summer the same appetite returns a little free cooling and dehumidification. The cleanest installations feed the machine semi-conditioned air; the arithmetic here prices the meter either way.

Held against the resistance page, this page is one half of an argument. The floor of unity guarantees the comparison its sign before any number is entered; what remains open is the size of the discount, which the saving page reads with both bills on one screen.

When this calculation is used

• Pricing a heat-pump water heater’s year before it is installed, from the household’s hot-water load and the label’s uniform-energy-factor-type rating.
• Re-pricing an installed unit’s year after a tariff change, holding the load and the rating constant while only the price moves.
• Feeding the comparison: this cost is the challenger’s side of the saving the trio computes on its own page.

Worked example

Run the pack’s declared reference year: the same ordinary hot-water demand the resistance page prices, served instead by a heat-pump water heater at a typical uniform-energy-factor-type coefficient, on the same mid-range residential tariff.

The engine returns the annual cost and, separately, the electricity the unit drew to earn it. Read the gap between heat delivered and electricity consumed first: that gap is the heat gathered from the air around the tank rather than bought at the meter, and the whole reason this bill sits below the resistance benchmark for the same water.

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 coefficient toward unity, as a cold closet or relentless back-to-back draws would, and watch the bill climb toward the resistance benchmark — the floor for this machine is the ceiling for that one.

What each input represents

Assumptions and limits

• One year-average coefficient stands in for every season and every draw: cool surroundings, clustered demand and backup-element hours are already averaged into the single input.
• The heat the compressor gathers is treated as free. A tank inside the heated envelope borrows part of it from the space-heating bill in winter and returns a little cooling in summer — an interaction the relation does not price.
• One flat tariff prices every unit; time-of-use windows must be blended toward the slow, steady hours the unit actually recovers over.
• This is an operating cost only. The unit’s substantial purchase premium belongs to the payback siblings, fed by the saving this trio computes.

What the guards protect against

• The coefficient may not fall below unity, and the pack ships the refusal as a declared test vector: below unity the unit would deliver less heat than the electricity it draws — worse than the bare element it exists to beat — which describes a broken machine or a mistyped rating, not a heat-pump water heater.
• The coefficient is also capped above anything a tank-mounted compressor achieves, so a rating misread — an energy factor scaled a hundredfold, or a figure copied from marketing rather than the label — is refused rather than silently pricing an impossible year.
• The load must be positive and is bounded far above any household’s annual demand, catching watt-hours entered where kilowatt-hours belong.

Provenance

Heating-fuel cost-comparison method: cost of delivered heat as fuel price over efficiency, with the water heater’s efficiency read as its uniform-energy-factor-type coefficient of performance

The annual hot-water heat load is divided by the coefficient of performance to yield the electricity the unit consumes, and the tariff prices that electricity into an annual cost.

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.