Sizu Riatto
Watt Happens Next · Chapter 2

The Heating Line

One straight line through a month of reads tells you how leaky the house is and what tomorrow will cost. The slope is the heat loss; where the line starts is the hot water and cooking.

Home › Calculators › The Heating Line

Opens on the book's house. Change any number to your own and press Calculate.

The days: outdoor mean temperature and gas used (same order, commas or spaces)

Paste the daily temperatures and gas reads, then press Calculate.

The formula

  • x = degrees below the base = base − the day's mean outdoor temperature; y = the day's gas in kWh
  • The least-squares line y = a + b x: b = Σ(x − x̄)(y − ȳ) ÷ Σ(x − x̄)², a = ȳ − b x̄
  • a = gas a day with no heating (hot water and cooking); b = gas per degree-day
  • Heat loss (W per °C) = b × boiler efficiency ÷ 24 × 1,000
  • r² = 1 − (what the line misses)² ÷ (the spread)²: near 1, the line explains nearly every day
  • Tomorrow's gas = a + b × (base − the forecast mean), and just a when it is warmer than the base
The book's worked example, Chapter 2. The book's 28 days give 8.07 kWh per degree-day and 7.30 kWh a day with no heating, r² 0.97. So the heat loss is 8.066 × 0.9 ÷ 24 × 1,000 = 302 W per °C (573 Btu an hour per °F); the book rounds it to 300. A 4 °C day calls for 7.30 + 8.07 × 11.5 = 100.1 kWh of gas.
Check it. Call tomorrow's gas off the line tonight, then read the meter tomorrow at the same time: within 10% scores 2 points.

Honest limits. The line is a model of your house in the weather it has seen: wind, sun, a party or a week away move single days off it. Use whole days, read at the same time, and at least two weeks of them. The book's house, its meters and its bill were worked out on paper from published figures, not measured by us: read your own meters and log your own night. Tariffs are illustrative, as seen in November 2026 (shaped like the GB price cap of October to December 2026, with US prices beside), shown without a currency sign; put in your own. No saving is promised. Everything stays in your browser: no sign-up, nothing stored.

These calculators go with Watt Happens Next (Make It Add Up, Book 3), where every number on this page is worked by hand.