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Is there a formula for the amount of fish you can stock per galon tank and then the size and depth the grow bed can be?

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I'm going to answer with numbers for media based systems since that is what I know.

For beginners who need to ask how many fish they can stock, I usually say 1 fish (that might grow out to plate size) per cubic foot of media filled grow bed.  Since the amount of fish you can stock is really dependent on filtration capacity of the system.  But how much fish tank do you need for that fish?  Well if you are building a 1:1 system as in the grow beds are equal to the fish tank, then that would be about 7.5 gallons of fish tank per fish since it takes about 7.5 gallons to make a cubic foot (I know I'm rounding but it will due.)  Now if you have less grow bed than fish tank, well you should still only stock as many fish as your grow beds can filter for so that will simply mean more fish tank water per fish, this works to a point but if you are talking a swimming pool as fish tank but only a blue barrel as grow bed, well you may run into other problems being that out of scale.

Now you can have more grow beds than you have fish tank but then you need to make sure you have a way to keep the water level in the tank from fluctuating and making your fish too stressed about the air encroaching on their territory.  This might be done with a sump tank or some type of sequencing.  If you feel you are likely to want max fish, then you should aim for at least twice as much grow bed as you have fish tank so that you will have enough filtration and plant space to balance the waste production of the fish.  However, I still do not recommend max fish numbers to anyone who has to ask how many fish they can stock.

i've worked on a large raft system. we used the ratios 0.3lbs of fish mass / 1sqft of growing area. and 1 lb of fish / 1gal of water for the tank.

but remember, if you stock the fish tank with a bunch of baby fish, they will grow, and a thinning of the heard might be necessary, so always keep in mind the size the fish will grow to be as TCL suggested.

1 fish (or 1 lb of fish) per gallon of fish tank is definitely a number that I would avoid advertizing to any but fish keeping experts. 

I know of a few too many operations that have started off by putting 1 fish per gallon into a system and very quickly crashed.  I currently have 1 fish per 3 gallons (and most of those fish are probably going to be plate size at 1/3rd of a lb) and that feels like too many for a backyard operation when the water warms up.

When talking about 1 lb of fish per gallon of fish tank, you want monitoring of dissolved oxygen and staff on call in case anything goes wrong.

sorry, sorry sorry.

i've lost the ability to edit that post, but it should be 1 lbfish / 4 gal of water.

thank you TCL for catching that.

i dont know if i got caught up in numbers and put the wrong one down or just had a finger slip.

thanks, that sounds far more sane for most aquaponics.

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