The Science of Thermostat Setbacks: Degree-Hours and Heat Transfer Rates
A smart thermostat reduces heating and cooling energy consumption by implementing setbacks (lowering temperatures in winter or raising them in summer) during periods when occupants are asleep or away. The rate of heat transfer through walls and windows is directly proportional to the temperature difference between the interior and exterior environments. By narrowing this temperature gap for several hours, we reduce the rate of heat loss (or gain), lowering the runtime required by the furnace or air conditioner.
The calculator anchors its savings rate to the U.S. Department of Energy, which says you can save as much as 10% a year on heating and cooling by turning the thermostat back 7°F to 10°F for 8 hours a day. At the top of that range this is 1% of the bill per degree of setback held for 8 hours, so the calculator uses Savings % = min(10%, Δ T × H/8 × 1%) where Δ T is the setback in °F and H is the daily setback hours. Scaling linearly below 10°F and 8 hours is the calculator's own assumption, and the cap keeps it within DOE's figure.
You can compare these smart home savings with physical envelope upgrades using our home insulation savings calculator or see how system modifications reduce overall carbon outputs with the carbon footprint calculator. The calculator caps savings at 10% of your bill, DOE's own ceiling. DOE also notes that savings are larger in milder climates, and that setting back a heat pump in heating mode can cancel the savings, so treat the result as an upper-end estimate for a furnace or air conditioner.