Area, velocity and the only equation you need
Airflow is velocity times area. Written in the units the trade actually uses, with diameter in inches and area in square feet:
Area (sq ft) = π × (d ÷ 24)² and FPM = CFM ÷ area
An 8 inch round duct has an area of π × (8/24)², which is 0.3491 square feet. Put 400 CFM through it and the air is moving 400 ÷ 0.3491, or about 1,146 feet per minute. Halve the diameter and the area drops by a factor of four, so the velocity quadruples — which is why going from 6 inch to 4 inch flex to make a fitting work is never the small change it looks like.
Rectangular duct is the same idea with area equal to width times depth divided by 144. What is not obvious is how a rectangle compares to a round duct, and the answer is not equal area. A rectangle has more wall surface for the same area, so it has more friction, and a flat rectangle is worse than a square one. The standard way to handle that is the equivalent round diameter, the round duct that would carry the same flow at the same friction rate:
De = 1.30 × (ab)0.625 ÷ (a + b)0.250
This is the ASHRAE equal-friction, equal-flow equivalent diameter, and it is the one used on this page. An 8 by 8 square works out to 8.7 inches equivalent, not 8. A 20 by 8, which has two and a half times the area of that square, comes out at 13.5 inches equivalent rather than the 13.8 its area alone would suggest. The flatter it gets, the more of its area is wasted.
Velocity or friction rate
There are two ways to arrive at a size and they answer different questions.
Sizing by velocity asks how fast the air will be moving. It is intuitive, it is the right frame when noise is your main concern, and it is the only sensible frame for dust collection where the velocity itself is doing a job. Its weakness is that it says nothing about the pressure the fan has to produce, so a system sized entirely by velocity can still be a system the equipment cannot serve.
Sizing by friction rate asks how much pressure each hundred feet of duct will consume. You choose a budget, commonly somewhere around 0.08 to 0.10 inches of water gauge per 100 feet in residential work, size every duct in the system to that same rate, and the total is a straightforward matter of adding up the run lengths. This is the equal friction method and it is the basis of how real systems are designed. It falls out of the standard friction relation for galvanised duct:
Δp per 100 ft = 0.109136 × CFM1.9 ÷ d5.02
Four hundred CFM in that same 8 inch duct comes to 0.28 inches per 100 feet — well above a typical residential budget, which tells you that 8 inches is a fast, tight choice for 400 CFM even before anyone comments on the noise.
| Duct | Velocity commonly used | What happens above it |
|---|---|---|
| Residential supply branch | 600-900 FPM | Audible rush at the register |
| Residential trunk | 700-1,000 FPM | Noise carries into rooms off the trunk |
| Return duct | 500-700 FPM | Return grille whistle, which travels further than supply noise |
| Commercial main | 1,200-1,800 FPM | Needs lining or attenuation to stay tolerable |
| Dust collection branch | 3,500-4,000 FPM | Nothing bad — below it is the problem |
The noise you are buying when you go a size down
Duct noise comes from turbulence, and turbulence rises steeply with velocity — sound power from airflow scales roughly with the fifth or sixth power of velocity, which means small increases in speed are large increases in noise. Going from a 10 inch duct to an 8 inch duct on the same flow raises the velocity by about 56 percent, and the noise by considerably more than that.
Worse, most of what you hear is not the straight duct at all. It is the fittings: a sharp elbow with no turning vanes, a takeoff cut into the side of a trunk, a damper part-closed to balance a room, and above all the register or grille where the air has to change direction and slow down into the room. Undersize the duct and every one of those gets louder at once. The register is where complaints originate, and the register is downstream of every decision made in the duct.
Space is finite and sometimes the small duct is the only duct that fits. When that happens the useful moves are to keep it as short and straight as possible, to use long-radius elbows or vaned ones rather than sharp bends, to expand back up to a larger size before the register rather than blasting through a small boot, and to accept the noise on a run that serves a laundry rather than the one that serves a bedroom.
What is missing from this page
What this gives you is a sized duct, and duct is the easy part of a duct system. It does not do fittings, and in a real installation fittings are usually the majority of the pressure loss. It does not know how many feet of run you have, so it cannot total up a pressure the fan must overcome. It does not know what the equipment's blower can actually deliver against that pressure, which is the constraint that decides whether the system works. It does not balance flows between branches, and it does not know what each room needs in the first place — that comes from a load calculation, room by room, not from a duct chart. In the trade those are separate exercises with their own methods, and a residential system designed properly gets its loads from one and its duct layout from another. Use this to check a size, to compare two options, or to understand why the run someone else installed is noisy. For a system that has to work on the first try, the sizing is one input to a design rather than the design itself.
Questions people ask
What size duct do I need for 400 CFM?
It depends entirely on what the duct is for. At a residential supply branch velocity of around 700 FPM, 400 CFM wants roughly a 10 inch round duct. At a commercial main velocity of 1,500 FPM the same flow fits in 7 inches. As a dust collection branch at 4,000 FPM it needs only about 4.3 inches, and making it larger would be a mistake. Sized on a residential friction budget of 0.10 inches per 100 feet it comes out near 9.8 inches, which is why 10 inch is the answer people usually land on. The flow alone never determines the size; the flow plus the intent does.
Is round or rectangular duct better?
Round is better on every technical measure and rectangular exists because buildings have flat cavities. A round duct has the least wall surface for a given area, so the least friction, and it holds its shape and seals more easily. A rectangle of the same cross-sectional area always carries less, and the flatter it is the worse the penalty gets — which is what the equivalent diameter formula quantifies. The practical rule is to keep the aspect ratio at or below about 4 to 1, and closer to square wherever there is room for it. Where a duct has to pass through a joist bay or a 2x4 wall, rectangular is simply the shape that fits, and the friction cost is the price of the space.
What is a good friction rate for residential duct?
Somewhere around 0.08 to 0.10 inches of water gauge per 100 feet is the range in general use, but the honest answer is that the friction rate is an output of the design rather than a number you pick from a table. It comes from the external static pressure the equipment is rated for, minus what the coil, filter, grilles and registers consume, divided across the effective length of the longest run including all the fittings expressed as equivalent length. A system with a high-MERV filter and a long duct path has a smaller budget left for the duct than a simple one, so the correct friction rate for it is lower and its ducts are larger. Using 0.10 as a default is a reasonable starting assumption and a poor final answer.
Does flex duct need to be bigger than rigid?
Yes, and by more than most people allow for. Fully stretched flex duct with its corrugations relaxed already has substantially more friction than smooth rigid duct of the same diameter, because the inner liner is not smooth. That is the best case, and it is rarely what gets installed. Flex that is compressed to fit a space, or that sags between supports, or that turns a corner with a tight radius, can lose several times what rigid loses. The figures on this page are for galvanised rigid duct and do not include any allowance for flex. If a run is flex, size it generously, pull it tight, support it at close intervals and keep the bends wide.