The right negative pressure

My cabinet is 23 in. tall, 18 in. wide and 20 in deep. I have one 3.5" hole cut and the rest of it is pretty well sealed.

I have a 57cfm fan I was planning on using on the 3.5" hole but was wondering what size of a hole I need to make for the passive intake and still keep negative pressure.

a couple of inches should be adequate, unless the cabinet is air tight which i doubt it is, you probably won't even need to cut one.

what light do you have?

i read the rule of thumb for passive intake is double your exhaust size. id do two holes, one on each corner (on the bottom of the cab of course), 3 in diameter for each one, and use black nylon panty hose to stop light leaks

Thanks, guys, how do I test it?

in some cases with a strong fan, even double the exhaust fan size is not enough. you can put a tissue paper or something at the intake hole, if you feel suction is too strong, it is probably still too small. also you may notice fan noise going down as you shut the door, meaning that the hole is also too small