Insulation upgrade: the annual saving

What the climate pays for a tighter envelope

Degree-days are the climate compressed to one number: every degree the outdoor day sits below the base temperature, accumulated across the heating season. Multiply a conductance reduction by them — with the day-to-hours and watts-to-kilowatts bookkeeping the engine carries — and out comes the heat the envelope no longer loses in a year. The degree-day method is the standard first estimate of seasonal loss, and the whole saving is linear in it: harsher winters pay proportionally more for the same batts.

Where the degree-day figure comes from decides whether the answer means anything. Use the climate NORMALS for the site — the long-run average a weather service publishes — rather than one memorable winter, because a mild year understates the measure and a brutal one oversells it. The base-temperature convention matters too: published degree-days assume the heating switches on below a stated outdoor temperature, and a well-insulated, gain-rich house effectively runs a lower base than the convention. Match the published basis or expect the estimate to drift.

The heat never lost still has to be translated into energy never bought, and the heating system’s coefficient does the translating. Electric-resistance heat converts one-for-one, so every avoided kilowatt-hour of loss is an avoided kilowatt-hour on the meter; a heat pump made the heat at a multiple, so the same avoided loss removes proportionally less electricity. Efficient machinery and a tight envelope share one saving — the better the machine, the less each avoided unit was going to cost anyway.

The tariff is the final multiplier and the honest place to be careful. It is the per-kilowatt-hour price from the household’s own bill, not a national headline figure; time-of-use households should blend to the rate the heating actually pays, which for overnight-heavy heating can sit well below the daytime price. The relation as declared prices electric heating — a gas-heated house needs its avoided heat walked through fuel price and combustion efficiency instead, which is the furnace page’s territory.

The declared reverse workflow turns the question around: fix the annual figure the measure should earn, and the engine solves for the tariff that earns it. Read against the bill, that parity price says whether the local market already rewards the measure or whether the case rests on electricity getting dearer — a sensitivity the single forward answer cannot express.

When this calculation is used

• Pricing a retrofit’s annual worth once the delta page has produced its conductance reduction, with degree-days and tariff looked up for the actual site.
• Comparing the same measure across climates — a relocation, a rental portfolio, a second home — by moving only the degree-day input.
• Feeding the payback sibling: this annual figure is the denominator its years are made of.
• Solving backwards — the declared reverse workflow — for the electricity price at which the measure earns a chosen annual figure.

Worked example

Run the pack’s declared reference case: a solid conductance reduction of the size a real loft measure produces, 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 saving and, separately, the electricity never purchased. Read the kilowatt-hours against the household’s annual consumption first: the share of the year’s electricity the measure quietly deletes is the more durable headline, because it survives every future price change.

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 coefficient from resistance to a heat pump’s and the money shrinks while the physics stands — the machine had already banked most of it.

What each input represents

Assumptions and limits

• Seasonal loss is proportional to degree-days 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.
• The saving prices electrically heated homes — resistance or heat pump; combustion fuels need the avoided heat priced through fuel cost and efficiency instead.
• One flat tariff prices every avoided kilowatt-hour, though time-of-use plans pay different rates across the heating day.
• The reduction is taken as given and permanent; settling, moisture or workmanship that erodes the installed resistance erodes the saving with it.

What the guards protect against

• A zero conductance reduction is refused — the pack ships the refusal as a declared test vector — because pricing a measure that changes nothing would return a costless zero dressed as an answer instead of the data-entry error it is.
• The degree-day input is capped above any inhabited climate, catching degree-HOURS or a Fahrenheit-based figure pasted 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: avoided conductance times heating degree-days, with purchased energy scaled by system efficiency

The conductance reduction is multiplied by the annual heating degree-days — with the hours-per-day and kilowatt scaling carried in the relation — to yield the heat never lost, divided by the heating system’s coefficient to yield the electricity never purchased, and priced at the tariff; the declared reverse workflow solves for the tariff that earns a chosen annual 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.