sizing extraction fan and scrubber size?

i have a room, need to exhaust into air return on furnace or under the house.

how do i decide what sized extraction fan and carbon scrubber and duct work, i need?

thank you

You want to be able to empty all air in your room In about 3 minutes. For ex a 10x10x10 room has 1000 sqft of space inside. So take a fan thats 400cfm(cubic foot a minute) ×3 equal 1200 sgft in 3 minutes. Thats a basic fan setup .if you add on a carbon filter duct work etc etc then in my opinion you need a bigger fan. I am no ac guy so bare with me. But I go for 10cfm per 10ft of duct work. Carbon filter slows air down drastically. So a 10x10x10 room with 10ft of ducting plus filter I add 150cfm per filter. There is no theroritical reasoning or were I get my numbers I happen to read some things awhile ago and made up my own "that a boy" system. So personally i would run 700cfm fan w a 7-800cfm carbon filter and a good fan controller as I dont like my fans wide open as they get noisy. Thats my opinion if you ran fan at 3/4 speed you would be running roughly 500cfm which would be.plenty with everthing now yiur room is up to you

It also depends on intake air temps and how many btu your putting in the room with lights, dehumidification and the like.

always go big on fan filter combos. too much is still perfect, not enough and a sad panda you will be. speed controllers are cheap if its moving too much air.