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Size the fan CFM for the room volume, and then size the duct based on the duct length and the tables/charts from the fan datasheet (and the available duct fittings on the fan).  If it's a small bathroom, it will likely be a small fan with a 3 or 4 inch duct, and given the length you'd likely want to go with 4 inch duct. 4 inch is also the most common size for duct outlets (wall caps, etc) and other accessories too.

Depending on length, PVC or sheet metal is probably the way to go, and make a small slope down toward the wall cap to drain condensation.


Usually would want to plan this according to your joist direction, etc.


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