Duct Temperature Drop & Heat Loss Calculator
Enter a duct size, run length, airflow, temperatures, and installed R-value to estimate the leaving air temperature and heat transfer. The tool also solves backward for the R-value needed to hold the change under your target.
Leaving air temperature57.46
- Duct temperature change (°F)
- 2.46
- Heat gain or loss (Btu/h)
- 2,125.4
- Heat transfer per 100 ft (Btu/h)
- 4,250.81
- Exterior duct area (ft²)
- 266.67
- Required R-value for target change
- 9.88
- Entering temperature difference retained
- 96.22%
Positive temperature change means the duct air is gaining heat from the surrounding space.
Uses standard air at 0.075 lb/ft³ and 0.24 Btu/(lb·°F); leakage and fittings are not included.
How to use this calculator
- Choose rectangular or round duct and enter the outside dimensions for that shape.
- Enter the developed duct length exposed to the surrounding air temperature.
- Enter airflow, entering air temperature, surrounding temperature, and installed insulation R-value.
- Set the maximum acceptable temperature rise or drop to see the required R-value.
How the duct temperature drop is calculated
This calculator treats the duct run as a steady heat-transfer path between moving air inside the duct and the surrounding space. It first turns field dimensions into exterior area, then applies the exponential air-temperature equation used for insulated duct temperature-drop estimates.
For a rectangular duct, the outside perimeter is P = 2 × (W + H) ÷ 12, where width and height are in inches and perimeter is in feet. For a round duct, P = π × D ÷ 12. The exterior area is A = P × L, with length in feet.
The air heat-capacity rate is C = 1.08 × airflow. The factor 1.08 comes from standard air density, air specific heat, and 60 minutes per hour. With installed duct insulation R-value, the conductance is UA = A ÷ R.
The leaving air temperature is:
T2 = Ta + (T1 − Ta) × exp[-A ÷ (R × 1.08 × CFM)]
- T1 is the entering air temperature.
- Ta is the surrounding air temperature.
- T2 is the leaving air temperature after the exposed run.
The heat transfer shown is the sensible load magnitude: Q = 1.08 × CFM × |T1 − T2|. A positive duct temperature change means the air warmed along the run; a negative change means it cooled. The calculator also reports the same load normalized to 100 feet so ducts of different lengths can be compared.
What moves the result most
Longer ducts, larger perimeters, lower installed R-values, and lower airflow all increase the temperature change. Airflow matters because more air mass can carry the same heat transfer with a smaller temperature shift. Shape matters through perimeter: two ducts with the same airflow can have different exposed area and therefore different heat gain or heat loss.
Solving for a target R-value
To size insulation for a maximum allowed temperature change, the same equation is solved backward. The calculator builds a target leaving temperature in the direction of the surrounding air, then uses R = -A ÷ {C × ln[(Ttarget − Ta) ÷ (T1 − Ta)]}. If the entering air already matches the surroundings, there is no heat transfer and no finite R-value to solve for.
What this calculator leaves out
This is a sensible-heat, steady-state estimate. It does not include duct leakage, fittings, equipment cabinets, solar radiation, condensation, humidity effects, altitude corrections, or changing attic and crawlspace temperatures along the run. Split a duct into separate sections when size, airflow, insulation, or surrounding temperature changes materially.
Worked example
Suppose a 20 in by 12 in rectangular supply duct runs 50 ft through a 120°F attic. Air enters at 55°F, airflow is 800 cfm, and the installed duct insulation is R-8.
The perimeter is 2 × (20 + 12) ÷ 12 = 5.33 ft, so the exterior area is 5.33 × 50 = 266.67 ft². The heat-capacity rate is 1.08 × 800 = 864 Btu/(h·°F). The exponent is -266.67 ÷ (8 × 864) = -0.0386, giving a leaving air temperature of about 57.46°F.
That is a 2.46°F heat gain and about 2,126 Btu/h, or 4,251 Btu/h per 100 ft. To keep the change to 2°F with the same duct and airflow, the required installed insulation is about R-9.88.
Common questions
How much temperature does supply air lose through an attic duct?
For cooling supply air in a hot attic, the air usually gains heat rather than loses it. The amount depends on duct area, length, installed insulation R-value, airflow, and the temperature difference between the air and the attic. Longer ducts with low airflow and low R-value show the largest change.
How does airflow affect duct temperature change?
Higher airflow reduces the temperature change for the same duct and surroundings because more air mass is carrying the heat transfer. Lower airflow lets the air spend more effective time approaching the surrounding temperature, so the leaving temperature moves closer to ambient.
What R-value keeps duct temperature change below 2°F?
There is no single R-value that works for every duct. The required R-value rises when the duct is longer, the perimeter is larger, the airflow is lower, or the surrounding temperature is farther from the entering air temperature. Use the target temperature change field to solve this for the run you are checking.
Why is the leaving temperature equation exponential?
The driving temperature difference gets smaller as the air approaches the surrounding temperature. Each bit of duct length transfers heat based on the remaining difference, so the result is an exponential approach rather than a straight-line change.
Does this calculator include duct leakage?
No. It only estimates sensible heat transfer through the insulated duct surface. Leaks can add or remove air, change the delivered airflow, and mix in surrounding air, so a leaky duct can perform much worse than this surface-only estimate.