A setback is an area, and the ramps are not in it
The rule of thumb everybody has heard is some percentage saved per degree of setback per some number of hours. It is not wrong, but it silently assumes the house is at the setback temperature for the whole period, and a house is a thermal mass rather than a switch. It takes hours to get down and hours to come back, and during both of those it is somewhere in between.
Draw it and it is a trapezoid. Down the falling side at the drift rate, flat along the bottom, up the recovery side. The saving is proportional to the area of that shape, and the two ramps each contribute only half of what their duration would suggest, because the average depth across a linear ramp is half its end value.
On the defaults — 6 F of setback, 1.5 F/h of drift, 3 F/h of recovery, a nine-hour absence with recovery starting on return — the fall takes 4 hours, the flat section is 5 hours, and the recovery takes 2. The area is 12 plus 30 plus 6, which is 48 degree-hours. The flat assumption would have said 6 times 9, or 54. So you get about 89 percent of what the rule of thumb implies, which is close enough that on a nine-hour absence the rule of thumb is basically fine.
Short absences are where it falls apart
Now run the same house for a two-hour errand. The fall takes 4 hours and you only have 2, so the house never gets below 3 F down. There is no flat section. The area is a triangle down of 3 degree-hours and a triangle back up of 1.5, for 4.5 in total, against the 12 that a flat 6-degree assumption would claim. That is 37.5 percent — you got just over a third of the saving you thought you were getting, from a setback that felt identical on the thermostat.
The page works the threshold backwards. With these rates, an absence has to be about 5 hours before the realised area reaches 80 percent of the assumed one. Below about 4 hours the house has not even arrived at the setback temperature. That is the useful decision: not whether to set back, but whether this particular absence is long enough to be worth the recovery.
The rates are what move that threshold, and they move it a long way. A leaky house with a drift of 3 F/h reaches the setback in 2 hours instead of 4, so short setbacks work far better there. A house with a slow recovery — which is the common situation with a heat pump in genuinely cold weather — has a long ramp back, and a long ramp back is dead area no matter how long the absence was.
Pre-heating trades money for comfort, and the trade is visible
Switch the mode to recovery starting early and the same nine-hour window gives 4 hours down, 3 hours flat and 2 hours up, all inside the window: 12 plus 18 plus 6, or 36 degree-hours. That is 67 percent of the flat assumption rather than 89, so pre-heating costs you a quarter of the realised saving.
What it buys is that the house is comfortable when you walk in, instead of spending two hours climbing while you are in it. That is not a bad trade and it is not a free one, and the two numbers on screen let you decide rather than assume. Note also that the two modes have different cycle lengths — 11 hours against 9 — because in the return mode the recovery happens outside the window rather than inside it.
Everything here is degree-hours. To turn it into money you need a rate and a degree-day figure, which is the heating cost savings calculator. The right way to combine them is to take the dollar figure from that page and multiply it by the ratio from this one.
Questions people ask
Is it true that setting the thermostat back does not save anything?
No, but the common version of the claim points at something real. The saving is smaller than the flat rule of thumb suggests, because the two ramps deliver half the area their duration implies. On a nine-hour absence with the default rates you still get 89 percent of the assumed saving, which is plainly worth having. On a two-hour errand you get about 37 percent, which usually is not.
How long does a house take to recover from a setback?
Depth divided by your recovery rate, and the recovery rate is something you measure rather than look up. Six degrees at 3 F/h is two hours. The same six degrees at 1 F/h, which is not unusual for a heat pump on a cold day, is six hours, and that changes the whole calculation because six hours of ramp inside a nine-hour window leaves almost no flat section to save anything.
How do I measure drift and recovery?
Once each, on a cold day, with a thermometer and a clock. Note the indoor temperature, turn the heat off, wait two hours, note it again, and divide the drop by two for the drift rate. Then turn it back on from that lower temperature and time how long it takes to climb back for the recovery rate. Both change with outdoor temperature, so measure on a day resembling the ones the setback is meant for.
Should recovery start before I get home?
That is a comfort decision with a visible price. On the defaults, pre-heating drops the realised saving from 48 degree-hours to 36, about a quarter. In exchange the house is at temperature when you walk in instead of taking two hours to get there while you are in it. Both figures are on the page so you can choose rather than guess which way the trade falls for you.
Where are the dollars?
Deliberately absent, because turning this into money needs your fuel, your rate and a degree-day figure for your location, and there is already a calculator for that. This page gives the physical ratio — how much of the assumed area you really get. Take the dollar saving from the heating cost savings calculator and multiply it by that ratio, and you have a figure that accounts for the ramps instead of ignoring them.