Why the answer is an exponential and not a subtraction
Air moving down a duct in a colder space loses heat at a rate set by how far it is above that space. As it cools, the difference shrinks and the loss slows, so the temperature approaches the surrounding air along a curve rather than dropping at a fixed number of degrees per foot. The whole run collapses to one exponent: the conductance of the duct divided by the heat capacity flow rate of the air.
Work the default through. Thirty feet of 8 in round has 62.8 square feet of outer surface. R-8 of wrap plus 0.68 of outside film is 8.68 of resistance, so the conductance is 7.24 Btu per hour per degree. Four hundred CFM of standard air carries 432 Btu per hour per degree. The ratio is 0.0168, the exponential of minus that is 0.9834, and the air closes 1.66 percent of the 80 degree gap — it arrives at 118.7 F having entered at 120, and 574 Btu per hour went into the attic.
Airflow is the input people forget
Insulation is where attention goes and airflow is where the sensitivity is. Drop that same run from 400 CFM to 150 — a branch with the damper most of the way shut, or a blower on a low tap — and the exponent nearly triples. The air now closes 4.4 percent of the gap and arrives at 116.5 F. The heat crossing the wall barely changes at 567 Btu per hour, because the duct is the same duct in the same attic, but the drop at the register goes from 1.3 degrees to 3.5 — two and a half times as far.
This is the mechanism behind a familiar complaint: the far room is cold, someone chokes the near branches to push more air to it, and the far room gets marginally more air at a noticeably lower temperature. The two effects partly cancel and the occupant is unimpressed.
The outside film is a bigger share than it looks
Bare sheet metal in still attic air has essentially only the film, around 0.68. Wrapping it with R-4 takes the total to 4.68 and cuts the loss from 6,655 Btu per hour to 1,058 — to about a sixth. Going from R-4 to R-8 takes the total from 4.68 to 8.68 and cuts it to 574, by 46 percent rather than by half. The first layer is doing an enormous amount of work and each subsequent layer does less, which is the reason the page prints both R-values side by side rather than a rule about which is right.
The same arithmetic explains why compressed wrap is worse than it seems. Insulation strapped tight over a joist or squashed where the duct passes a truss is not at its label thickness at those points, and heat crosses at the thin places preferentially.
What it does not know
Leakage. A duct that loses 574 Btu per hour through R-8 wrap and dumps five percent of its air into the attic is losing roughly 1,730 Btu per hour out of the joints as well, and the joints are not in this arithmetic at all. Conduction is the tractable part; leaks want a pressure test.
It also does not know your attic. Attic temperature is entered once and held for the whole run, and a real attic swings sixty degrees through a summer day, gets warmer near the ridge, and is warmed locally by the duct itself. Treat the answer as the run at that one condition, and run the page twice — once for a design winter morning and once for a design summer afternoon — rather than looking for one number that covers both.
Questions people ask
How much heat does an attic duct lose?
For thirty feet of 8 in round at R-8 carrying 400 CFM of 120 F air through a 40 F attic, about 574 Btu per hour, and the air arrives 1.3 degrees cooler than it left. The two numbers move differently: the heat depends on the duct and the attic, while the temperature drop depends on how fast the air is going through it. Slow the same duct to 150 CFM and the drop goes from 1.3 degrees to 3.5 while the heat stays near 567.
Why does the temperature drop follow a curve rather than a straight line?
Because the loss at any point depends on how far the air still is above the surrounding space, and that gap shrinks as the air cools. The result is an exponential approach to the temperature of the attic or crawl space, set by the duct conductance divided by the heat capacity flow of the air. Doubling the length does not double the loss, and halving the airflow doubles the exponent.
Does going from R-4 to R-8 halve the duct loss?
No, and the reason is the outside air film. There is roughly 0.68 of resistance on the outside of the jacket before any insulation, so R-4 of wrap is 4.68 of total resistance and R-8 is 8.68. The loss falls by about 46 percent, not 50. Going from bare metal to R-4, by contrast, cuts it by 84 percent, which is why the first layer is worth so much more than the last.
Will an insulated duct sweat in an attic?
That is not a question arithmetic can settle, and this page does not try. It reports the jacket surface temperature the resistance split implies and puts it beside the dew point you enter, as a margin in degrees. Whether condensation actually forms depends on the humidity through the whole day, on whether the vapour barrier is continuous and sealed at every joint and boot, and on what happens at the fittings where the wrap is thinnest.
Should I count duct that is buried in attic insulation?
Not as part of this length. Duct buried under blown insulation is in a different thermal situation, with a resistance that depends on the depth and the coverage over it and a moisture situation of its own. Enter only the length that is exposed to the unconditioned air, and treat buried runs separately.