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Duct Heat Gain and Loss Calculator

Ducts in a hot attic or a cold crawlspace gain or lose heat through their insulation. Enter the duct, its R-value and the temperatures to see the heat and the change in air temperature.

Method reviewed October 26, 2026. Version 1.0.0. How it works

This is an estimate. It uses a simplified method and typical assumptions, all listed below. Use it to plan and to check quotes; equipment should be sized from a full room-by-room load calculation (ACCA Manual J) by a qualified professional.

Your inputs

Unit system
Duct shape

The installed R-value printed on the duct jacket or insulation (for example R-4.2, R-6 or R-8). Compressed insulation performs below its label.

Example: a summer attic. Use your own measured or design value.

Thinner air at altitude carries less heat per CFM. Leave at 0 for sea-level (standard-air) results.

Result

Heat gained by the air
870BTU/h
Air temperature leaving the duct
60.4°F
Temperature change along the duct
5.37°F

This duct gains about 870 BTU/h; the air warms from 55 °F to 60.4 °F.

  • Duct leakage often costs more than conduction through the duct wall — seal joints as well as insulating.
Simple estimate UA × (T_around − T_in)
908BTU/h
Duct surface area
83.8ft²
UA (area ÷ R)
13.96BTU/h·°F
Show the working
  1. Duct surface area = perimeter × length
    25.13 in ÷ 12 × 40 ft = 83.8 ft²
  2. UA = area ÷ R
    83.8 ÷ 6 = 13.96 BTU/h·°F
  3. Air capacity rate = 1.08 × density ratio × CFM
    162 BTU/h·°F
  4. Leaving air T = T_around + (T_in − T_around) × e^(−UA ÷ capacity rate)
    120 + (55 − 120) × e^(−0.0862) = 60.37 °F
  5. Heat = capacity rate × (T_out − T_in)
    162 × 5.37 = 870 BTU/h

How it works

Heat flows through the duct wall at a rate of surface area ÷ R-value × temperature difference — the same conduction equation used for walls. The air carrying it changes temperature at 1.08 BTU/h per CFM per °F.

Because the air warms (or cools) as it travels, the temperature difference shrinks along the duct. The calculator solves the two equations together, which gives an exponential approach to the surrounding temperature. A simpler estimate that holds the entering temperature constant is shown alongside; it slightly overstates the heat.

What to enter

  • The length that runs outside the conditioned space
  • The installed insulation R-value printed on the duct jacket or wrap; compressed insulation performs below its label
  • The temperature around the duct: a summer attic is often far hotter than outdoors, so measure or use your design value

What it leaves out

Leakage often costs more than conduction: air lost from a supply duct in the attic is conditioned air thrown away. The calculator also ignores radiation from a hot roof deck and condensation on cold ducts. Sealing and insulating ducts, or moving them inside, addresses all of these.

Worked example

These are the example values the calculator opens with, and the result the engine calculates for them.

Inputs

Duct shape
Round
Duct diameter
8 in
Length outside the conditioned space
40 ft
Duct insulation R-value
6 h·ft²·°F/BTU
Air temperature entering the duct
55 °F
Temperature around the duct
120 °F
Airflow in the duct
150 CFM
Site elevation
0 ft

Result

Heat gained by the air
870 BTU/h
Air temperature leaving the duct
60.4 °F
Temperature change along the duct
5.37 °F
Simple estimate UA × (T_around − T_in)
908 BTU/h
Duct surface area
83.8 ft²
UA (area ÷ R)
13.96 BTU/h·°F

This duct gains about 870 BTU/h; the air warms from 55 °F to 60.4 °F.

Assumptions

  • Heat flows through the duct wall at U = 1/R per square foot of duct surface (perimeter × length); surface films and the extra outside area of the insulation are ignored.
  • The air temperature changes along the duct, so the exact solution of Q = U·A·ΔT together with Q = 1.08·CFM·ΔT is used (an exponential approach to the surrounding temperature). The simple constant-temperature estimate is shown for comparison.

Limitations

  • Ignores leakage, radiation to and from the roof deck, and condensation on cold ducts.
  • Steady conditions; attic temperatures change through the day.

Frequently asked questions

How much heat does an attic duct gain?

For 40 feet of 8-inch R-6 duct carrying 150 CFM of 55 °F air through a 120 °F attic, about 870 BTU/h, warming the air by about 5 °F. Longer, bigger or less-insulated ducts gain more.

Does higher R-value always help?

Yes, heat flow falls in proportion to R. Going from R-4.2 to R-8 roughly halves conduction, though leakage and the duct’s location matter as much.

Why does lower airflow make the air change temperature more?

The same heat is spread over less air. Low airflow in a long attic run can lose much of its cooling before it reaches the room.

Sources

  1. Heat Loss from Buildings — The Engineering ToolBox. Conduction heat loss Q = U·A·ΔT with U = 1/ΣR.
  2. Regional Line Card — air-side formulas — Trane. Sensible = 1.08 × CFM × ΔT; latent = 0.68 × CFM × Δgr; total = 4.5 × CFM × Δh, with the derivation of each constant.
  3. Compression Effects on Pressure Loss in Flexible HVAC Ducts — B. Abushakra, I. S. Walker & M. H. Sherman, Lawrence Berkeley National Laboratory (2002). ASHRAE classes fabric-and-wire flexible duct as “rough”, 0.0035–0.015 ft (1.0–4.6 mm) fully extended; compression raises effective roughness far above that range.

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