The number on the box is one point on a curve
A fan does not have an airflow. It has a relationship between airflow and the pressure it is working against, and that relationship is the fan curve. At zero pressure, which is a fan sitting on a bench blowing into a room, it moves the most air it will ever move. As the resistance in front of it rises, flow falls. Where it falls to depends on the shape of the curve, which is a property of the fan.
The duct has a curve too, in the opposite direction. At low flow it takes almost no pressure to push air through the run; friction rises roughly with the square of velocity, so as flow increases the pressure required climbs steeply. Plot both on the same axes and they cross once. That crossing is the operating point: the only flow at which the fan is producing exactly the pressure the duct requires. It is what the fan actually delivers, and it is what this calculator solves for.
Why two fans with the same rating behave differently
Manufacturers publish airflow at a stated static pressure, and the stated pressure matters as much as the airflow. A fan quoted at 110 CFM at 0.1 inches of water gauge and a fan quoted at 110 CFM at 0.25 are not comparable products, and on a real duct run the second one will win by a wide margin.
The slope between two published points tells you how the fan behaves under load. A fan that drops from 90 to 70 CFM between 0.1 and 0.25 inches is losing about 133 CFM per inch of static, which is a fairly steep curve typical of a small axial fan. A better centrifugal unit loses much less over the same span. On a short straight duct the difference barely shows. On twenty feet with three elbows it decides whether the bathroom clears or stays foggy.
Where the system static comes from
| Component | How it scales | What moves it most |
|---|---|---|
| Straight duct | Length times friction rate | Diameter, by roughly the fifth power |
| Elbows | Equivalent length added | How tight the bend is, and whether it is flex |
| Flex compression | Multiplier on the friction rate | Whether the duct was stretched at install |
| Termination | Rises with the square of flow | Damper stiffness, screen, lint or leaves |
The diameter term dominates almost everything else. Going from four inch to six inch duct on the same run cuts the friction rate by roughly a factor of eight at the same flow, which is why the comparison rows on the results are usually the most useful part of the output. Many bathroom fans ship with a four inch outlet and will accept a six inch transition, and where the attic allows it that is generally the cheapest airflow available.
Elbows and where they sit
Every turn costs, and the equivalent length attributed to an elbow varies enormously with its geometry. A long radius metal elbow is a modest fitting. A tight bend formed by pushing flexible duct round a truss is not, and there is a common failure pattern where the duct leaves the fan housing, immediately turns ninety degrees to get out of the joist bay, and then turns again to reach the wall. Two hard bends within a foot of the fan disturb the flow at exactly the point where the fan is trying to establish it.
Set the equivalent length per elbow from a fitting table if you have one. Where you do not, the useful exercise is to run the calculation twice with a low and a high figure. If the answer changes the decision, the elbows are the thing to look at on site.
The part the airflow number does not cover
Bathroom exhaust removes moisture, and moisture leaves in the air, so the total moved matters as much as the rate. A fan delivering 60 CFM for thirty minutes moves 1,800 cubic feet; the same fan for five minutes moves 300. In a 560 cubic foot bathroom that is the difference between three air changes and half of one, and the mirror clearing is not the same thing as the wall cavity drying.
Which is why run time is usually the higher-value change. A timer, a humidity-sensing switch, or a fan on its own switch that gets left on is worth more than upsizing. The airflow calculation on this page tells you whether the fan can do the job at all; run time tells you whether it finishes it.
For the air change target itself, the CFM and air changes calculator covers the rate side across room types in more detail. If any of the run is flexible duct, the flex duct penalty calculator gives you a defensible multiplier for the field above. And where a house has several exhaust appliances running at once, the range hood makeup air calculator covers what happens to the house pressure when they all pull together.
Questions people ask
Why does my 110 CFM bathroom fan not seem to move 110 CFM?
Because 110 was measured at a static pressure your duct almost certainly exceeds, and often at zero. Take the worked default on this page: a fan rated 90 CFM at 0.1 inches and 70 at 0.25, on twenty feet of four inch duct with three elbows and a wall cap, lands at about 70 CFM at roughly a quarter inch of static. That is not a defective fan; it is the fan doing exactly what its published curve says it does when asked to work against that much resistance. The same fan on six inch duct over the same run comes out near 89 CFM. Nothing changed except the duct, and the duct is where nearly all of the difference lives.
Is it better to buy a bigger fan or a bigger duct?
Duct, in most cases, and it is not close. Friction falls with roughly the fifth power of diameter, so a single nominal size increase can cut the system resistance by most of its value, and the fan then operates far higher on its own curve at no extra running cost or noise. Putting a larger fan on the same restricted duct pushes it up a steeper part of its curve, so a fan rated fifty percent higher typically delivers far less than fifty percent more, while drawing more power and making more noise. Change the duct first, the elbows second, the termination third, and only buy a different fan when the duct is as good as the building allows.
What static pressure should I assume if the fan only publishes one number?
If a product publishes a single airflow figure with no stated static pressure, treat that as information about the product rather than as data. Fans intended for real duct runs publish a curve or at least two points, commonly at 0.1 and 0.25 inches of water gauge, because that is what an engineer needs. Where you only have one point, you can still bound the problem: enter that figure as point one, then enter a pessimistic second point and see how much the answer moves. If the operating point is sensitive to an assumption you had to invent, that is a reason to choose a fan whose manufacturer tells you what it does.
Does the termination really matter that much?
It can be a surprisingly large share of the total, especially on short runs, and it is the part most likely to get worse over time. A spring-loaded backdraft damper that has stiffened, a cap with an insect screen that has filled with dust, or a soffit vent partly blocked by insulation all add resistance at the point where the flow is trying to leave. Because termination loss scales with the square of flow, the effect grows fast as you push more air at it. It is also the only part of the system you can inspect from outside with a ladder, so it is worth checking before assuming anything about the fan.
Can I vent a bathroom fan into the attic or a soffit?
Where exhaust ducts are permitted to terminate is set by the code your jurisdiction has adopted and by the official enforcing it, so that question has a local answer rather than a general one. What is worth understanding physically is why the question comes up: air leaving a bathroom is warm and carries a lot of water vapour, and delivering that into an attic in winter puts it against cold sheathing where it condenses. A soffit termination has a related issue, in that soffits are often intake vents for the attic, so exhaust discharged there can be drawn straight back in. Attic ventilation and moisture are covered separately by the attic ventilation calculator. For where a specific duct may terminate on a specific building, ask the building department rather than a calculator.