Duct heat loss calculator

How the heat flow of a duct is worked out

This page treats a round duct as a cylinder with three resistances in series, the air film inside, the insulation wrapped around it and the air film outside. The sum is the total R-value on the inner surface. Dividing the inner area of the whole run by that R-value gives its conductance, and the heat flow follows from the temperature difference to the surrounding air. The method is from a published paper on the true R-value of round residential duct, with the sensible heat equation of ACCA for the air. It is an estimate for a sales call or a quick check, not a permit-grade calculation.

Total resistance

R_total = R_in + R_actual + R_out x (d_i / d_o)For the default 6 inch R-8 duct at 499 FPM the inside film is R-0.49, the insulation R-5.62 and the outside film R-0.34 once it is referred to the inner surface, so the total is R-6.45. The outside film is R-0.667 before the diameter ratio, from 1.0 radiant plus 0.5 convective Btu/h-ft2-F.

Insulation on a cylinder

R_actual = 2.8 x (d_i / 2) x ln(1 + 2t / d_i), with t = labeled R / 2.8The label rates flat insulation. Around a round duct the outer layer is longer than the inner one, so the same thickness is worth less. R-8 is 2.86 inches thick at R-2.8 per inch and works out to R-5.62 on a 6 inch duct, 30 percent under the label before the films are added.

Inside film

R_in = d_i / (k x Nu), Nu = 0.023 Re^0.8 Pr^0.35The inside film depends on the air speed and the diameter, and faster air has a thinner film. 98 CFM is 499 FPM in the 6 inch duct, which gives R-0.49. Air properties are those of 69 F air at sea level, as in the paper.

Conductance of the run

UA = L x (pi x d_i / 12) / R_total25 ft of 6 inch duct has 39.3 sq ft of inner surface, and divided by R-6.45 that is 6.09 BTU/h-F. Each degree of difference between the air and the attic moves that many BTU/h at the start of the run.

Heat flow and air temperature

Q = 1.08 x CFM x (T_in - T_out), T_out = T_amb + (T_in - T_amb) x exp(-UA / (1.08 x CFM))The air changes temperature as it travels, so the heat flow is a little below UA times the inlet difference. In the default run the duct passes 385 BTU/h, the air leaves at 58.6 F, 3.6 F from where it started, and the inlet estimate reads 396 BTU/h. Air density 0.075 x specific heat 0.24 x 60 makes the 1.08, for sea level air.

Code check

labeled R vs R-8 for ducts of 3 inches and largerThe model energy codes set R-8 for supply and return ducts of 3 inches and larger outside conditioned space, and R-6 for smaller ducts. This page compares the labeled value, as the code does, and prints the total R-value beside it.

Worked examples

The default case is 25 ft of 6 inch R-8 duct carrying 98 CFM, which is 499 FPM, with 55 F air in a 120 F attic. Inside, the air film is R-0.49. The 2.86 inch wrap works out to R-5.62 around the cylinder, and the outside film adds R-0.34 when referred to the inner surface, which makes R-6.45 in all. With 39.3 sq ft of inner surface, the run conducts 6.09 BTU/h-F. At the inlet difference that is 396 BTU/h, and with the air warming along the run the duct gains 385 BTU/h and the air leaves at 58.6 F. That is the whole method. Every other case below only changes diameter, wrap, airflow, length or the two temperatures, and each one is rerun through the same function, so a result that looks odd can be traced back to one of those five inputs.

Strip the wrap. The same run is R-1.16 in total, gains 1,888 BTU/h and changes the air by 17.8 F. The six inch R-8 values come from Table 1 of the Ecotope paper, which prints R-5.62 for the insulation and R-6.45 in total at 500 FPM. Eight cases run through the same function the form uses are in the table below.

Sources and data

• Palmiter and Kruse (Ecotope), True R-Values of Round Residential Ductwork, ACEEE 2006 Summer Study - The thermal model of a round duct, with the total R-value as the sum of the inside film, the insulation as installed around a cylinder and the outside film at R-0.667, the Nusselt correlation for the inside film, and UA as length times inner area per foot over the total R-value. Its Table 1 gives the R-values of 14 diameters and four ratings at 500 FPM, and this page reproduces all of them to within 0.006, which is the rounding of the printed table. It states that a six inch R-8 duct is R-5.62 without the films and R-6.45 with them.
• ACCA, The Physics of Heat and Air Flow - The sensible heat equation BTU/h = 1.08 x CFM x temperature change, with the 1.08 built from an air density of 0.075, a specific heat of 0.24 and 60 minutes per hour, and the caution that it holds for air near sea level and room temperature.
• IECC 2021 R403.3.1 and 2024 R403.3.3, duct insulation outside conditioned space (text as reprinted by UpCodes) - The minimum for supply and return ducts outside conditioned space, R-8 for ducts 3 inches in diameter and larger and R-6 for smaller ducts. Its section number moved between editions, and states amend it, so the adopted text decides.
• New York State Department of State, Technical Bulletin TB-7006, Duct Location and Insulation Requirements - A state reading of the same requirement under the 2025 New York code, with a minimum of R-8 for ducts 3 inches or larger and R-6 for ducts under 3 inches, and the ways ducts in an unconditioned attic or wall can be treated.

Limitations of this calculator

• The method is for round duct, flexible or metal with an insulating wrap, from 4 to 28 inches. Rectangular duct has a different surface and film, and is not calculated.
• The insulation is taken at R-2.8 per inch, which is how the source table is built. A product with a different R per inch has a different thickness, and its own data sheet and the installed thickness decide.
• Air properties are fixed at 69 F and sea level, and the film coefficients are constants. The source says their variation has a minor effect on the total, and the 1.08 factor changes with altitude and air density.
• Only heat conduction through the duct wall and insulation is counted. Air leaking out of the duct and the heat it carries are not, and a leaky duct can lose far more than conduction does. The duct leakage calculator covers the test limits.
• In cooling mode the page counts sensible heat gain only. Latent gain and condensation on the outer surface are not calculated, and a cold supply duct in a humid space needs a vapor retarder.
• The surroundings are one temperature you type. A real attic swings through the day, and radiant heat from the roof deck and wind change the outside film. Bare galvanized or foil has a smaller radiant coefficient than the dull surface assumed here, and a bare duct far from the surrounding temperature has a larger convective one.
• Plenums, boots, fittings, hangers and the metal wall are left out, and so are runs buried in ceiling insulation or in the ground, which have their own rules in the energy codes.
• Air velocity must fall between 300 and 2,500 FPM, because the inside film formula is for fully developed turbulent flow. Slower or faster runs are refused with the CFM that fits the diameter.
• The code comparison reads the labeled R-value against the model code minimum. Edition, local amendments and special cases such as ducts in conditioned space or inside insulated assemblies decide what is required.
• This is preliminary estimating of duct heat flow, not a permit-grade load calculation. A Manual J and Manual D design, and the judgment of the contractor on the job, come first.

Common duct heat loss mistakes

1. Reading the label as the total R-value. R-8 is the rating of flat insulation. On a 6 inch duct the layer alone works out to R-5.62, and the two air films add R-0.83, so the whole duct is R-6.45, 19 percent under the label. Using R-8 in the calculation understates the heat flow.
2. Leaving the duct bare or the wrap thin. A bare 6 inch duct has only the two films, R-1.16 in total. The default run then moves 1,888 BTU/h against 385, 4.9 times as much, and the air changes by 17.8 F. With R-4.2 the figure is 564 BTU/h, and with R-11 it is 319.
3. Using the inlet temperature difference on a long run. UA times the inlet difference holds for a short run. On 200 ft of the same duct it reads 3,165 BTU/h, while the air that has already warmed up carries 2,537 BTU/h. The longer the run, the less the simple figure holds.
4. Treating the air temperature change as the same at any airflow. The heat flow changes little with airflow, but the temperature change does. Here the default run changes the air by 3.6 F at 98 CFM and 2.4 F at 150 CFM, because the same heat is spread over more air.
5. Counting leakage as heat loss, or leaving it out. This page counts heat conducted through the duct wall. Air that leaks out of the duct is a separate loss, and a duct can pass a conduction check while it leaks badly. Check the duct leakage test as its own item.
6. Taking the code minimum as the design target. R-8 is the floor in the model energy codes for ducts outside conditioned space. In the default attic it still gains 385 BTU/h over 25 ft, and R-11 gains 319. Weigh the extra wrap against the load and the cost of the run, and keep the ducts inside the envelope where the plan allows.

Common questions about duct heat loss

Related calculators

• Duct leakage test calculator The air that leaks out is the other duct loss, and this page does not count it.
• Duct velocity and friction calculator Velocity and friction loss for a round duct at a given airflow.
• HVAC CFM calculator The airflow for the load, which sets the velocity used here.
• Insulation R-value calculator Total R and heat loss of a wall, ceiling or floor from its layers.
• All tools Every public BuildSolver calculator in one list.

Used on the same job

• Duct sizing calculator The round duct size for the airflow of a run.
• Rectangular to round duct calculator A round equivalent for a rectangular duct.
• Furnace temperature rise calculator Supply and return temperatures at the furnace, where the duct run starts.