Sizu Riatto
Watt Happens Next · Chapter 5

Adding Up the Slices

Energy is the area under the power graph. Add up the slices and a day of half-hourly readings becomes its kWh, a washing-machine cycle becomes its cost, and a cold night becomes the heat the house lost.

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

Power readings: the area under them is the energy

Degree-hours: the area under the gap between indoors and out

Enter power readings or a night's temperatures, then press Calculate.

The formula

  • Rectangles: Σ power × the slice's width (hours). For a smart meter's averages this is exact
  • Spot readings: left sum uses each slice's first reading, right sum its last; the trapezoid rule averages the two
  • Σ says "add them all up"; the integral ∫ is what the sum becomes as the slices get thinner
  • Degree-hours = the area under (indoor − outdoor) against hours, by trapezoids
  • Heat lost (kWh) = heat loss (kW per °C) × degree-hours; check: the heat store (heat loss × τ) × the drop
The book's worked example, Chapter 5. The book's weekday, 48 half hours: 9.2 kWh by rectangles, with a base of 180 W all night and a half-hour peak of 1.28 kW from 18:00. The night's gap gives 127.6 °C·h by trapezoids, so the house lost 0.3 × 127.6 = 38.3 kWh; the heat store says 10.8 × 3.5 = 37.8 kWh. They agree within 2%.
Check it. Put a plug meter on one washing-machine cycle and write its watts every 5 minutes: the trapezoid sum should land near the plug meter's own kWh total.

Honest limits. A slice sum is only as fine as its slices: a 5-minute spike between two readings is invisible. The degree-hour check uses a steady outdoor temperature; wind and sun move it. 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.