At the common design friction rate of 0.10 in. w.g. per 100 ft, 400 CFM needs a 10 in round duct: the exact answer is 9.83 in, and at 10 in the air moves at 733 feet per minute with 0.092 in of friction per 100 ft. The rectangular equivalents are 12 × 8 in, 10 × 10 in or 16 × 6 in.
How the duct size is calculated
By friction rate (equal friction method). Every duct in the system is sized so it loses the same pressure per 100 ft. The calculator solves the round galvanized duct friction equation published by Engineering ToolBox for the diameter:
Friction (in. w.g./100 ft) = 0.109136 × CFM^1.9 ÷ d^5.02, so d = (0.109136 × CFM^1.9 ÷ friction)^(1 ÷ 5.02)
For 400 CFM at 0.10: d = (0.109136 × 400^1.9 ÷ 0.10)^(1/5.02) = 9.83 in. The calculator rounds up to the next common size and reports the velocity and friction at that size.
By velocity. The diameter that carries the airflow at a chosen speed:
d (in) = √(4 × CFM ÷ (π × velocity in fpm)) × 12
400 CFM at 700 fpm gives 10.24 in, so a 12 in duct, where the air slows to 509 fpm.
Rectangular duct equivalents
A rectangular duct matches a round one when its Huebscher equivalent diameter is the same: the diameter of the round duct with the same friction at the same airflow.
De = 1.30 × (a × b)^0.625 ÷ (a + b)^0.25
An 8 × 12 in duct works out to 10.66 in, which matches the 10.7 in in Engineering ToolBox's table. The calculator finds, for each common height (6, 8, 10 and 12 in), the width in 2 in steps whose equivalent diameter reaches the required size. Flat, wide ducts lose more to friction than their area suggests, which is why a 16 × 6 in duct (96 sq in) only matches a 10.4 in round duct (85 sq in).
CFM capacity of round ducts at 0.10 in. w.g.
| Diameter | CFM at 0.10 | CFM at 0.08 |
|---|---|---|
| 4 in | 37 | 33 |
| 5 in | 67 | 60 |
| 6 in | 109 | 97 |
| 7 in | 163 | 145 |
| 8 in | 232 | 207 |
| 9 in | 317 | 282 |
| 10 in | 419 | 372 |
| 12 in | 678 | 603 |
| 14 in | 1,019 | 906 |
| 16 in | 1,450 | 1,290 |
| 18 in | 1,980 | 1,760 |
| 20 in | 2,615 | 2,325 |
These come straight from the friction equation for smooth galvanized pipe. Flex duct has more friction per foot, especially when it sags or is compressed, so a flex run usually needs the next size up.
Which friction rate to use
Energy Vanguard explains that the friction rate is not a constant: it is the blower's available static pressure × 100 ÷ the total effective length of the longest run, fittings included. Its worked example has 0.31 in of available pressure over 424 ft of effective length, which gives 0.073, and it warns that the often assumed 0.10 can leave ducts too small. Use 0.08 as a general supply value when you have nothing better, and the calculated figure once you know the blower and the layout.
Velocity limits
ACCA Manual D's recommended maximums, quoted by Energy Vanguard, are 900 fpm for supply ducts and 700 fpm for returns. Faster air is noisy at the registers. The velocity check under the result flags a duct over the limit for the type you pick. For ducts in an unconditioned attic, Energy Vanguard cites designer Mike MacFarland's lower targets: 600 to 750 fpm for exposed ducts, 400 to 600 for ducts buried in insulation.
Getting the CFM right first
The duct is only as right as the airflow you size it for. A room's share of a system is usually its share of the cooling load; the whole system moves about 400 CFM per ton (Trane). Work the airflow out in the CFM calculator, or let the ductwork calculator split the system airflow between rooms and size the trunk and every branch at once. For the tonnage behind it, see the AC size calculator; for heat-only systems, the furnace size calculator gives the furnace that sets the blower. To size a single room's cooling or heat before any of this, start with the BTU calculator.
This ductwork sizing calculator gives the round duct diameter for each run from its airflow; the CFM calculator finds the airflow itself.