what size fan do i need for my grow closet ?

my plants are in the grow box (closet) and doing ok but it sure gets hot in there with the doors closed so i have to leave them open a little during lights on. I would like to keep the doors closed as its a stelth grow but dont know what type of fan to purchase.
The space is: 5ft high x 3ft width x 2ft depth and i am using a 400 HPS. The grow box (tub) is aprox 1ft high in that space.
I can cut vent holes for the fan/fans ducting in the sides or top of the
wardrobe/closet and vent the hot air out of the room but need some info on what fan to use and what m3/hr it has to vent to keep the temp down.
have attatched pics to give an idea of the closet size with the doors open. sorry but they are not very good.
my thoughts are that the space is too small to vent well . And with a 400 hps in there it would still get too hot with the doors shut.
advice needed and greatly appreciated.

I can circulate fish tanks really well, so maybe this type of knowledge will translate for you.

First, you want to calculate your volume in cubic feet. Then, I think that a turnover rate of about 3x the volume per hour might be a good place to start. So, if your space is 30'cu, then you'd want a fan (or fans) that would turn over about 90cfm (cfm = cubic feet per minute, I learned this outfitting our kitchen and had to size a range hood). This is my own approximation, not a hard and fast rule, but I think it's a good place to start.

In any event, use the fan as an exhaust, do not put one fan as an intake and one as outlet, use one or both as outlets and use negative pressure and large enough intakes for the flow. Does that make sense?

thanks for your help. this does help a lot. not sure what the m3 is but will try to work it out. There must be a table or chart somewhere on the web to give me an idea.
I would also have to vent the hot air outside the room the closet is in so i dont suck the same air back in again. lol

If you have access, then put the exhaust up into your attic. Even better if you can tie into an existing attic exhaust, so it vents outside. I don't know what m3 means. To the best of my knowledge exhaust and ventilation fans are rated in cfm only (cubic feet per minute), not by the hour. 90cfm should be relatively easy to find.
Check this shit: Nutone Exhaust Fan 90 cfm 4" duct. Can you make something like this work?

to vent to the loft would mean cutting a 4" hole in my cealing and i dont fancy that. but i could vent through an open window.
nice bike....

Thank you, here's another shot.

(I truly love my bike. I'd tell you her name, but it's a little unique and I'm rather active online. Not having work does that.)

And if you take a look at that fan, it has an opening on the side, ready-made for you to connect up duct-work.

she is very nice