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When building an aquaponics system in general, what is the best equation to use to determine fish loads (waste generation) to grow bed (filtration) ratios. Is it a simple calculation of pounds of fish to gallons of water processed by the grow bed? Or pounds of fish to gallons of water held in the grow beds?

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The thing that matters most here are biomass producing ammonia, and surface area for bacteria in the grow beds to live on -- there must not be too much ammonia produced for the bacteria to handle, otherwise the fish will be stressed and later harmed.

A good rule of thumb I've seen (links escape me right now) is 0.03Kg of fish per litre of growbed volume, or 30 kg / m3.

The solids filtration is obviously still important, but as long as these get filtered/settled out by the grow media or other filtration, all is good. The setting capacity of a growbed depends on the media in there, plus the flow rates and type (constant flood vs flood/drain etc).

Caveat: Like all rules of thumb, you can certainly deviate from this 30 kg fish / m3 growbed figure, but the limitations will depend on many factors like temperature, oxygenation, pH, flow rates and other improvements to the system. Commercial aquaponics systems will stock lot above this figure because they do extra filtration and water quality management.

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