Two methods, and which one applies depends on the size of the room.

Method 1 — floor area
For bathrooms under about 100 square feet: 1 CFM per square foot, with a minimum of 50 CFM.
A 7 × 9 bathroom is 63 square feet, so 63 CFM, and the nearest standard fan is 80.
Simple, and it is what most bathrooms use.
Method 2 — by fixture
For bathrooms over 100 square feet, or with several fixtures, add an allowance per fixture:
| Fixture | CFM |
|---|---|
| Toilet | 50 |
| Shower | 50 |
| Bath | 50 |
| Jetted tub | 100 |
A primary bath with a toilet, a shower and a jetted tub is 50 + 50 + 100 = 200 CFM.
Where the toilet is in a separate compartment, it needs its own fan rather than counting toward one.
Round up, then check the duct
Fan ratings are measured at a low static pressure, and real ducting always adds more. A fan rated 80 CFM in a laboratory delivers considerably less through 15 feet of flexible duct with two elbows.
Sizing up one step is normal and sensible. Sizing up two steps to compensate for a bad duct is fixing the wrong thing.
The duct is where fans actually fail
Rigid duct, not flexible. Flexible duct has ridges, sags between supports, and can lose half the rated airflow over a short run.
As short and straight as possible. Every elbow costs airflow equivalent to several feet of straight duct.
Correct diameter — usually 4 inches for a small fan and 6 for a larger one. Reducing a 6-inch fan to a 4-inch duct wastes the fan.
Insulated where it runs through an unconditioned attic, or warm moist air condenses inside the duct and drips back down through the fan.
Sloped slightly toward the outside, so any condensation drains out rather than back.
It must terminate outside
Not into an attic, not into a soffit, not into a crawl space. Venting into an attic delivers the bathroom's moisture to the roof structure, and it is one of the more common causes of attic mould and sheathing rot.
Terminate through a roof cap or a wall cap with a damper, and check that the damper actually opens — they are frequently painted shut or blocked by insulation.
Soffit venting is a special case: many soffit vents draw air back into the attic through the intake vents beside them, which defeats the purpose. Where a soffit termination is used, it needs to be a proper terminal well clear of the intakes.
Run time matters as much as size
A fan that runs during the shower and stops when the light goes off has not removed most of the moisture, because the room keeps evaporating for a long time afterwards.
Twenty minutes after the shower ends is a common recommendation. A timer switch or a humidity-sensing switch does this without anyone remembering.
Humidity-sensing fans that run automatically are the most effective option in practice, because they respond to the condition rather than a schedule.
Sound
Rated in sones — lower is quieter. Below 1.0 sone is very quiet, and above 3 is loud enough that people avoid using it.
A fan nobody turns on removes no moisture at all, so sound rating is a functional specification rather than a luxury.
The quick check on an existing fan
Hold a sheet of tissue against the grille with the fan running. It should hold firmly against it.
If it falls, the fan is failing or the duct is blocked or disconnected, and a disconnected duct in an attic is dumping bathroom air into the roof space.
