Annual heating cost by the degree-day method

What the whole bill says that the deltas cannot

The chain runs in one direction. The whole-house conductance says how much heat the envelope leaks per degree of indoor-outdoor difference; the degree-days say how much difference the climate accumulates across a season; their product — with the day-to-hours and watts-to-kilowatts bookkeeping the engine carries — is the heat the house loses in a year. Dividing by the heating system’s coefficient turns lost heat into purchased electricity, and the tariff turns electricity into the bill.

What distinguishes this page from its siblings is that nothing here is a difference. The setback page and the insulation page each push a delta through exactly this chain; this page owns the level. The level is where honesty gets tested: run the house as it stands and set the answer against a real winter’s bills. If they disagree badly, the conductance or the degree-day figure is wrong — and every delta priced through the same chain inherits that error silently.

Both upstream inputs have homes of their own. The conductance comes from an energy audit or from the pack’s roll-up calculator, which sums the envelope’s parts — walls, roof, glazing, air leakage — into the single figure this page consumes. The degree-days come from the weather service’s climate normals for the site, not one remembered winter, and they carry a base-temperature convention: published figures assume the heating switches on below a stated outdoor temperature, which is also where the model quietly concedes solar and internal gains.

The coefficient and the tariff close the chain the way the sibling pages describe at length: unity for electric resistance, the seasonal average for a heat pump, and the per-unit price from the household’s own bill, blended toward the hours the heating actually runs. The defaults the pack ships for the later inputs are illustrative only — the conductance is the one figure this page refuses to guess for you.

The declared reverse workflow asks the question that turns this page into a target. Fix the annual bill a household is prepared to tolerate, and the engine solves for the whole-house conductance that delivers it under the stated climate, machine and tariff. That implied conductance is an envelope specification — set it against the roll-up of the house as built, and the gap is the retrofit programme, stated in the same units the insulation pages already trade in.

When this calculation is used

• Estimating a season’s heating bill before it happens — a prospective house, a first winter, an electrification plan — from an audited or rolled-up conductance and the site’s climate normals.
• Validating the model against reality: running the house as it stands and comparing the answer with actual bills, before trusting any saving priced through the same chain.
• Establishing the baseline the delta pages perturb, so a quoted saving can be read as a share of the bill it comes off.
• Solving backwards — the declared reverse workflow — from a tolerable annual bill to the whole-house conductance that achieves it.

Worked example

Run the pack’s declared reference house: a whole-house conductance of the size an ordinary detached home carries, in a mid-severity heating climate at a mid-range residential tariff, with electric-resistance heat converting one-for-one.

The engine returns the annual cost and, behind it, the season’s heat loss and the electricity purchased to cover it. Read the heat loss against the electricity first: at resistance the two coincide, and every gap that opens between them when the coefficient rises is warmth the machine moved rather than made.

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. Move the climate input from a mild site’s normals to a harsh one’s and the bill scales in exact proportion — the linearity every saving page in this pack leans on.

What each input represents

Assumptions and limits

• The house is one zone losing heat steadily through one constant conductance: solar gain, internal gains and occupancy are presumed folded into the base-temperature convention the degree-day figure was published against.
• One season-average coefficient stands in for the whole winter; a heat pump’s cold-snap derating and defrost cycles are already averaged into the single input.
• The relation prices electrically heated homes — resistance or heat pump; a combustion-heated house needs its season walked through fuel price and burner efficiency on the furnace page instead.
• One flat tariff prices every kilowatt-hour, though time-of-use plans pay different rates across the heating day.

What the guards protect against

• A zero degree-day figure is refused — the pack ships the refusal as a declared test vector — because a climate with no accumulated cold has no heating season to price, and a costless zero would dress missing data up as an answer.
• The conductance must be positive and is capped far above any dwelling, catching wrong-unit figures or a district’s worth of building pasted into a house-sized relation; the degree-day input is likewise capped above any inhabited climate, catching degree-hours or a Fahrenheit-based figure entered where Celsius degree-days belong.
• The tariff band refuses prices quoted in cents entered as dollars, and the coefficient’s band refuses fractions describing a machine that wastes most of its electricity — mistyped decimals, not heating systems.

Provenance

Degree-day heat-loss estimation: envelope conductance times heating degree-days, with purchased energy scaled by system efficiency

The whole-house conductance is multiplied by the annual heating degree-days — with the hours-per-day and kilowatt scaling carried in the relation — to yield the season’s heat loss, divided by the heating system’s coefficient to yield the electricity purchased, and priced at the tariff; the declared reverse workflow solves for the conductance a stated annual bill implies.

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.