The ratio, not the rule
Heat leaves a house roughly in proportion to the difference between inside and outside temperature. That is the whole mechanism, and every rule of thumb about thermostat settings is a simplification of it. If the house is held at 70°F while it averages 30°F outside, the system is bridging 40 degrees. Set it to 68 and the gap becomes 38. The heating demand falls by two divided by forty, or five percent, and it does so for as long as the lower setting holds.
This is why the same two-degree change is worth wildly different amounts in different places. In a mild winter averaging 50°F outside, going from 70 to 68 cuts a twenty-degree gap to eighteen, a ten percent saving. In a hard winter averaging 10°F, the same change moves a sixty-degree gap to fifty-eight, worth about three percent. The outdoor-temperature method in this calculator does that division directly. The percent-per-degree method applies a fixed figure instead, which is easier to quote and less true.
Where the percent-per-degree numbers come from
Energy agencies commonly express setback advice as a percentage saved per degree over a sustained period — figures around one to three percent per degree Fahrenheit circulate widely, usually attached to a specific setback depth and duration. They are averages taken across housing stock and climates, and they are useful for a rough answer when you have no idea what your average outdoor temperature is. They are not a property of your house. If you know your climate, use the ratio method and you will get a better answer with less faith required.
The calculator compounds the percentage rather than multiplying it, so eight degrees at three percent is not 24 percent but about 22. Compounding is the right shape: each degree acts on what remains, not on the original.
Setback for part of the day
Most people do not lower the thermostat permanently. They lower it overnight, or while the house is empty. The hours field handles this by scaling the saving to the fraction of the day the lower setting actually holds — eight hours of setback is a third of the day and, to a first approximation, a third of the saving a permanent change would give.
To a first approximation, because recovery costs something. When the setting comes back up, the system runs longer to reheat the structure. The energy that went into the fabric of the house during the warm hours partly leaked away during the cold ones and has to be replaced. This is smaller than intuition suggests in a house with forced air and a correctly sized furnace, which is why setback saves money in practice as well as theory. It is larger, and can approach cancelling out, with slow-responding systems: hydronic radiators and especially radiant floors take hours to change the room, and cycling them daily through a deep swing gets you discomfort at both ends for very little.
Heat pumps are a different problem
Everything above assumes the cost of a unit of heat is constant. For a furnace or a boiler that is close enough to true. For a heat pump it is not: efficiency falls as the outdoor temperature drops, so the same unit of heat costs more on the coldest days — exactly the days when the demand is highest. And most heat pumps have resistance backup heat that engages on a large call for heat, which costs several times more per unit than the compressor does.
The practical consequence is that deep setbacks can backfire on a heat pump. A large recovery triggers the backup heat, and an hour of resistance heating can cost more than the setback saved overnight. Manufacturers generally advise either shallow setbacks or none, and modern thermostats designed for heat pumps ramp the recovery slowly to avoid calling the backup. If you have one, treat the numbers on this page as an upper bound and check what your thermostat is actually doing during recovery.
Reading the table before you change anything
The degree-by-degree table is there to make one comparison easy: the first two degrees against the last two. They are worth roughly the same amount of money, and they are not worth the same amount of discomfort. Most households find the first couple of degrees essentially free — a sweater, and nobody notices — and the sixth and eighth degrees genuinely unpleasant. Take the saving where it is cheap in comfort, put the rest of the effort into the envelope, and check the season figure rather than the month figure before deciding anything, because a change worth eight dollars a month is worth forty a winter and that is a different conversation.
Questions people ask
How much does turning the thermostat down one degree actually save?
It depends on your climate, and the dependence is strong enough that a single number would be misleading. The physical answer is one degree divided by the difference between your indoor setting and the average outdoor temperature. At 70°F indoors and 50°F outdoors that is one in twenty, or five percent. At 70°F indoors and 10°F outdoors it is one in sixty, under two percent. Widely quoted rules of thumb land around one to three percent per degree because they average across climates. Use the outdoor-temperature method here with your own winter average and you get an answer specific to where you live rather than to a national aggregate.
Is it cheaper to keep the heat steady or turn it off when out?
Lowering it is cheaper, and the intuition that says otherwise rests on a real effect that is smaller than it feels. The house loses heat in proportion to the temperature difference, so every hour spent cooler is an hour of reduced loss. Reheating does cost energy, but only enough to replace what leaked during the cooler period — it never exceeds the saving in a conventional system. The exceptions are worth knowing: heat pumps, where a large recovery can trigger expensive backup heat, and slow radiant systems that cannot recover in reasonable time. For a furnace with forced air, setting it back while out is straightforwardly cheaper.
What temperature should I actually set?
That is a comfort and health question rather than an arithmetic one, and this calculator deliberately does not answer it. What is worth knowing is where the floor is. Sustained cold indoor temperatures carry real health risk for infants, older people and anyone with a respiratory or cardiovascular condition, and cold surfaces plus normal indoor humidity produce condensation and mould on the coldest walls before anyone feels dangerously cold. There is also a plumbing floor: pipes in unheated crawlspaces, garages and exterior walls freeze at settings that feel merely chilly indoors. Below roughly 60°F, treat further reductions as something to think about rather than something to just do.
Why does my saving not match what the calculator says?
Most often because the monthly heating cost entered was not purely heating. A gas bill covers the water heater and often the range, and both continue regardless of the thermostat, so scaling the whole bill overstates the saving. Subtracting a summer bill from a winter one gets you much closer. Beyond that, weather does not repeat: a winter that runs five degrees colder than the last one will raise the bill through a change you made to lower it, and only a comparison normalised by heating degree days separates the two effects. And if the house has a heat pump, the assumption that a unit of heat has a constant price is not true, which breaks the arithmetic in both directions depending on the day.