Backyard Aquaponics
A place to discuss aquaponics

>> My question is: is there a way to calculate the fish to plant ratio before even purchasing anything?

have a look at the FAO publication "Small-scale aquaponic food production"
The links break these days so you will need to google around for the PDF.
It is discussed in there.

There are also some threads on this forum that get pretty specific.
TCLynx has one discussion from memory, and maybe Steve - try the search.

The issue is there are big differences simply due to system design, species of fish, age/stage/size of fish and what they get fed.
So there is not one number that can be computed that works for any setup.
At commercial scales you need to pay attention to aquaculture type issues and rely more and more on filtering for example.
Hence in a BYAP setup the tendency is for rules of thumb get thrown around
(and sadly not all of them are logical - eg the ratio of bed to fish tank is not really that relevant since it is all about fish and what the system can manage - as you note in your question at top)

simplest answer is stock conservatively and learn from your first year what your system can cope with.
too many calculations and claimed stocking rates are simply ludicrous - and people wonder why it goes bang and all the fish die.

I posted a question elsewhere about adding 1 extra IBC to my single chop & flip system. Is there anything obviously wrong with the diagram below? Any simple upgrades I could add before I start cutting? (radial flow separator is not to scale)

I think the basic concept should work as long as heights of things and pipe sizes are good (to make sure you don't overflow the fish tank or anything like that.

Make sure you install a top up valve just below your normal "low water level" in the sump since if it is installed too high you will keep overflowing and if installed too low, your pump may risk running dry.