The maths of overfeeding: what a gram of fish food does to your water

You are not feeding fish. You are feeding a nitrogen budget.

Here is the fact that makes the whole subject tractable: nitrogen is conserved. Every gram of food you drop in is a small parcel of nitrogen, and that nitrogen cannot vanish. It ends up in exactly four places — built into fish as growth, breathed out as ammonia, banked as nitrate, or physically removed by you. Feed more nitrogen than your tank can send to those sinks, and the surplus shows up as the thing that hurts fish: ammonia now, nitrate later.

That is the real definition of overfeeding, and it is a number, not a vibe. To find it, we only need to know two things about the food and a little about the tank.

What one gram of flake actually contains

Take your example: a flake food listing 45% crude protein, and a modest pinch of 0.5 g.

• Protein in that pinch: 0.5 g × 0.45 = 0.225 g
• Nitrogen in that protein: 0.225 g × 0.16 = 0.036 g = 36 mg of nitrogen

That 36 mg is the total nitrogen entering the tank from one small feeding. Nothing you do changes that total — filtration, plants and water changes only decide where it goes and how fast. To see why overfeeding is dangerous, follow those 36 mg to their destinations.

Eaten, digested, or rotting: three very different journeys

When a fish eats and digests a meal, aquaculture nutrition studies that build full “nitrogen budgets” consistently find the intake splits roughly three ways. The exact figures depend on species, food quality, temperature and how fast the fish is growing, but the shape is remarkably stable:²³

Where the nitrogen goes (when eaten)	Typical share	From our 36 mg
Retained as fish growth (locked into body protein)	~25–35%	~11 mg
Excreted as ammonia across the gills (mostly within a day)	~50–60%	~20 mg
Passed as faeces (undigested), mineralising to ammonia later	~10–15%	~5 mg

So even when a meal is eaten perfectly, well over half of its nitrogen returns to the water as ammonia — the bulk of it excreted straight across the gills within about a day of the meal, with the smaller faecal fraction mineralising to ammonia more slowly over the following days.⁴ Fish are ammonotelic: they excrete most of their nitrogenous waste as ammonia rather than urea, which is why the water bears the cost almost immediately. The only nitrogen that genuinely leaves the water-column budget is the fraction turned into fish flesh.

Now the same gram, uneaten

Uneaten food is where the arithmetic turns nasty, and for a reason people rarely state precisely. When food is eaten, ~30% of its nitrogen is removed from the water by being built into the fish. When food rots untouched, that sink disappears — there is no growth to lock nitrogen away, so effectively all of its nitrogen ends up as ammonia. Because eaten food surrenders only about two-thirds of its nitrogen to the water while uneaten food gives up essentially all of it, uneaten food yields on the order of a third to a half more ammonia per gram — the exact figure tracks whatever growth-retention fraction you assume, but the direction is not in doubt.

And that is only the nitrogen half. Rotting food is also a large dose of organic carbon, which feeds heterotrophic bacteria. Those bacteria multiply explosively, consuming oxygen as they go — the classic bacterial bloom that turns water milky, dragging down dissolved oxygen exactly when the ammonia is peaking. So uneaten food is a double hit: more ammonia, delivered more slowly and messily, on top of an oxygen crash. This is why “a whole tub in the water column” is genuinely dangerous in a way that a slightly generous pinch is not.

Why the same food is a different event in a 25 L and a 250 L tank

Here is the part that decides whether that ammonia matters. A quantity of ammonia is not a concentration until you divide by a volume — and concentration is what a fish’s gills actually feel. Take a full 1 g of the same 45% flake, left uneaten, so all of its 72 mg of nitrogen eventually becomes ammonia. Watch what the tank size alone does to it:

Tank volume	Ammonia produced (as TAN‑N)	Verdict
25 L (nano)	2.88 mg/L	Acutely dangerous
50 L	1.44 mg/L	Harmful
100 L	0.72 mg/L	Stressful
250 L	0.29 mg/L	Marginal — often survivable

The identical gram of food is a tenfold different event between a 25 L and a 250 L tank, purely from dilution. In the nano it lands at nearly 3 mg/L of total ammonia nitrogen; in the 250 L it barely reaches 0.3. For context, chronic stress in sensitive community fish tends to appear as total ammonia climbs past a few tenths of a mg/L, and the truly toxic form — free, un-ionised NH₃ — is only a small fraction of that total, set by pH and temperature.⁵ A warm, alkaline nano tank pushes more of that ammonia into the toxic free form and concentrates it, which is why small hard-water tanks are the least forgiving of a heavy hand.

Dilution is a genuine, quantifiable buffer — but notice it is the only thing volume buys you against the peak, and it works both ways. The same tenfold concentration factor applies to nitrate build-up:

Tank volume	Nitrate added per gram of food (fully converted)
25 L	~12.8 mg/L NO3
100 L	~3.2 mg/L NO3
250 L	~1.3 mg/L NO3

(Each 1 mg of nitrogen becomes 4.43 mg of nitrate ion once nitrified.) A nano tank therefore climbs toward a nitrate problem more than nine times faster per gram than a large tank — and it has less water to soften every other swing too: temperature, pH and oxygen all move faster in a small body of water. Volume is not just dilution; it is stability.

What the filter does — and the one thing it can’t

If volume sets the peak, the biofilter sets how fast that peak is cleared. A mature filter is a colony of nitrifying microbes that oxidise ammonia to nitrite and then nitrate. Crucially, that colony processes ammonia at a rate — it does not act instantly, and it cannot exceed the capacity it has grown to. Three consequences fall straight out of that:

• A bigger filter clears the peak faster, not lower. The ammonia still spikes to whatever the volume dictates; more biomedia and bacteria just pull it back down more quickly. Fish still feel the initial jump.
• The colony is sized to your recent feeding. Nitrifying bacteria are slow to multiply — days, not minutes. Suddenly double the food and the filter cannot keep pace until the population catches up, which is exactly why a jump in feeding causes an ammonia (then nitrite) spike a few days later, even in an established tank.
• The filter converts nitrogen; it never removes it. Every milligram of ammonia the filter “deals with” becomes a milligram of nitrogen as nitrate. A flawless filter running forever still leaves you with a rising nitrate line. This is the piece a bigger filter can never fix.

So the filter and the volume answer different questions. Volume asks how high does ammonia peak? The filter asks how quickly does it come back down? And nothing on this list actually gets nitrogen out of the tank. For that, there is exactly one export valve.

From ammonia to nitrate: the water-change arithmetic

Nitrate is where fed nitrogen accumulates, and the only routine ways out are plant uptake and water changes. That gives a clean steady-state sum. Suppose you feed 0.3 g/day of 45% flake to a small community, mostly eaten, so a bit under two-thirds of the nitrogen ends up as nitrate:

• Nitrogen to nitrate: 0.3 × 0.45 × 0.16 × ~0.65 ≈ 14 mg N/day → ~62 mg of nitrate ion per day.
• In a 100 L tank that is roughly +0.6 mg/L of nitrate every day, or ~4 mg/L a week.

A tank holds steady only when export matches production. A 30% weekly water change removes 30% of the standing nitrate, so the level settles where 30% of it equals a week’s production — around 14 mg/L in this example, before any plant uptake. Feed twice as much and that equilibrium doubles; do half the water changes and it doubles again. That is the “treadmill” hobbyists feel without naming: nitrate is simply the ledger of everything you have fed and not yet exported. A well-planted tank adds a second, faster valve, because fast-growing plants take up ammonium directly, skimming nitrogen off before it is ever nitrified.

So what actually is overfeeding?

Put the pieces together and a precise definition appears. Overfeeding is not a fixed amount of food. It is:

Which is why the honest answer to “how much can I feed?” is a system property, not a food property. A lightly stocked 250 L with a mature filter, heavy planting and weekly water changes can absorb a genuinely generous diet. A 25 L nano with a young filter and no plants cannot absorb the same pinch. Same food; different budget.

The variables that actually move the needle

Everything above reduces to a handful of levers. Roughly in order of impact:

Variable	What it changes
Fraction eaten	Biggest lever. Eaten food removes ~30% of its N as growth and delivers ammonia cleanly; uneaten food gives up ~40% more ammonia plus an organic-carbon oxygen crash.
Tank volume	Sets the peak ammonia concentration and the nitrate climb rate, roughly one-for-one. Also buffers pH, temperature and oxygen swings.
Amount fed & protein %	Together set the raw nitrogen input (protein × grams × 0.16). A 45% flake carries far more nitrogen per gram than an 8% algae wafer.
Filter maturity & size	Sets how fast ammonia is cleared and how large a feeding increase the tank can absorb before spiking. Does not lower the peak or remove nitrogen.
Plant load	A real export valve — fast growers consume ammonium directly, reducing both ammonia peaks and nitrate accumulation.
Water-change regime	The only reliable nitrate export. Sets the steady-state nitrate level for a given feeding rate.
pH & temperature	Decide what fraction of total ammonia is the toxic free NH3 form, and how fast food decomposes and fish metabolise. Warm and alkaline is the harshest combination.
Fish growth stage	Fast-growing juveniles retain more nitrogen as flesh, so a larger share of their food leaves the water budget; mature, non-growing fish retain less, so more of every meal returns as waste.

Myths, measured against the maths

“The food itself poisons the water.” No — the nitrogen does. A gram of nitrogen behaves identically whether it arrives as flake, bloodworm or fish waste. Food is dangerous only as a delivery vehicle for nitrogen and organic carbon.

“A bigger filter means I can feed more.” Partly. It lets you clear ammonia faster and absorb a bigger feeding without a spike — but it does nothing about nitrate, which still needs water changes or plants to export. Over-filtering an under-changed tank just gives you clearer water with a rising nitrate line.

“My planted tank can’t be overfed.” Plants raise the ceiling, they don’t remove it. Their uptake is finite and light-limited; exceed it and the surplus nitrogen simply passes through to nitrate and algae fuel like anywhere else.

“They act hungry, so they need more.” Appetite is not requirement. Most community fish are opportunistic feeders evolved to eat whenever food appears — behaviour that says nothing about how much nitrogen their tank can process.

“Uneaten food is bad because it rots.” True but incomplete. It is bad because it converts more of its nitrogen to ammonia than eaten food does (no growth sink), and because its organic carbon triggers an oxygen-hungry bacterial bloom. Rotting is the mechanism; the quantity is the point.

Putting numbers on your own tank

You do not need a chemistry set to use any of this — just the three habits the maths keeps pointing at.

• Feed to the fish, not the tank. The reliable heuristic remains what fish can clear in a couple of minutes with nothing settling on the substrate. That is the hobby’s rough proxy for “fraction eaten ≈ 100%”, which is the lever that matters most. (Our guide to feeding aquarium fish covers food types and portions in practice.)
• Scale the pinch to the volume, not your instinct. Remember the tenfold table: the same food is a different event in a nano than in a big tank. If you run small tanks, feed lighter and change water more often — the arithmetic gives you no slack there.
• Let nitrate be your scoreboard. Nitrate is the honest, integrated record of feeding minus export. If it creeps up week on week, you are feeding faster than you are exporting — the definition of overfeeding — regardless of how the fish look. A parameter log makes that trend obvious, and the nitrogen-cycle guide explains where every milligram is travelling.

“Don’t overfeed” turns out to be excellent advice hiding a precise idea: you are managing a nitrogen budget, and the only questions that matter are how much nitrogen you put in, how much of it goes into a fish, and how much water and export you have to spread the rest across. Get those three numbers roughly right and overfeeding stops being a mystery and becomes a sum you can win.

1. Mariotti, F., Tomé, D. & Mirand, P.P. (2008). Converting nitrogen into protein — beyond 6.25 and Jones’ factors. Critical Reviews in Food Science and Nutrition, 48(2), 177–184.
2. Bureau, D.P. & Hua, K. (2010). Towards effective nutritional management of waste outputs in aquaculture, with particular reference to salmonid aquaculture operations. Aquaculture Research, 41(5), 777–792.
3. Dosdat, A., Servais, F., Métailler, R., Huelvan, C. & Desbruyères, E. (1996). Comparison of nitrogenous losses in five teleost fish species. Aquaculture, 141(1–2), 107–127.
4. Timmons, M.B. & Ebeling, J.M. (2013). Recirculating Aquaculture (3rd ed.). Ithaca Publishing Company — on feed-derived ammonia loading and post-feeding excretion in closed systems.
5. Emerson, K., Russo, R.C., Lund, R.E. & Thurston, R.V. (1975). Aqueous ammonia equilibrium calculations: effect of pH and temperature. Journal of the Fisheries Research Board of Canada, 32(12), 2379–2383.
6. Randall, D.J. & Tsui, T.K.N. (2002). Ammonia toxicity in fish. Marine Pollution Bulletin, 45(1–6), 17–23.