Why the arithmetic is on show

Savings calculators usually produce a confident number from assumptions you cannot see. This one prints its working, because the assumption is doing most of the work.

The rule it uses — about one percent of the heating bill per °F of setback per eight hours a day — is the figure behind most published guidance, including the familiar advice that a 7 to 10 °F setback for eight hours saves around 10 percent a year.

It is a rule of thumb. It is not a model of your building, and the two biggest things it ignores are how well insulated your house is and how cold the winter turns out to be.

What moves the real figure

Insulation. A well-insulated house loses heat slowly, so it was spending less to hold the temperature and there is less to save. Counter-intuitively, the worse your house, the more a setback earns.

Thermal mass. A heavy masonry building coasts for hours after the heating goes off and takes hours to warm back up, which blunts short setbacks. A lightweight timber-framed house responds quickly and captures more.

How cold it is outside. Heat loss scales with the indoor-outdoor difference. The same 3-degree setback is proportionally worth more in mild weather and absolutely worth more in cold weather, because the underlying bill is bigger.

How long the setback lasts. Eight hours overnight is the standard case. Two hours barely registers, because much of it goes on cooling and reheating the fabric rather than on reduced loss.

The floor that overrides the saving

One hard limit, and it is not about money.

Below about −6 °C (20 °F) outdoors, the overnight setback is removing the margin that keeps the spaces around your pipes above freezing. On those nights, hold the daytime setting and give up the saving — a few pence against a burst pipe is not a trade worth making. The reasoning is in what temperature pipes freeze at.

For a house standing empty in winter, the floor is 13 °C (55 °F) and it does not bend.

Cheaper than any setback

Each of these lets you hold a lower temperature at the same comfort, which beats a schedule change:

None of those appear in the calculator, because they change the building rather than the schedule. They are usually the better place to start, and what setting to run once you have done them is in what thermostat setting for winter.