Calculating a Nutrient Solution: Working Out Milligrams per Litre from Label and Irrigation Water

A nutrient solution is the irrigation water once the fertiliser has been dissolved in it. Calculating a nutrient solution means working out, for each nutrient element, how many milligrams of it sit in one litre, that is how many thousandths of a gram, written mg/L. Two sources feed into the result: the fertiliser, whose content is printed on the label, and the water, which already carries something of its own. Whether the result fits only shows when it is set against target ranges, and those were measured in trials with one or two varieties per study.

A single line on the label shows how easily the sum goes wrong. Sulphur appears there as sulphur trioxide, SO₃, a compound of sulphur and oxygen in which only just over 40 % of the weight is sulphur. Anyone who enters the label figure as sulphur is therefore working with two and a half times what is actually in the bottle.

From label to milligrams

Fertiliser labels in the EU state phosphorus, potassium, calcium, magnesium and sulphur as oxides, meaning compounds with oxygen: P₂O₅, K₂O, CaO, MgO and SO₃. Think of it as a weight including the packaging, with the oxygen as the packaging. Only the contents count for the calculation, and fixed factors derived from atomic masses give them: P₂O₅ times 0.4364 gives phosphorus, K₂O times 0.8302 potassium, CaO times 0.7147 calcium, MgO times 0.6030 magnesium and SO₃ times 0.4005 sulphur. A label showing 10 % P₂O₅ therefore means a calculated 4.36 % phosphorus. Nitrogen is listed as the element itself, split by the forms in which it is present.

Liquid fertilisers add a second trap. Their content may be declared as a percentage by mass or by volume, that is relative to the weight or to the space the liquid takes up. Only a percentage by mass brings density into the sum, the weight of one millilitre: a fertiliser with 3 % nitrogen and a density of 1.2 g/ml delivers a calculated 72 mg/L nitrogen at 2 ml per litre of irrigation water if the 3 % is by mass, and 60 mg/L if it is by volume, a difference of one sixth. With solid fertiliser salts the content also depends on the commercial form: Epsom salt contains 9.9 % magnesium, kieserite, a magnesium sulphate holding less bound crystal water, 17.6 %. The product’s data sheet says which form it is.

What the irrigation water brings

Whatever is already dissolved in the water belongs to the nutrient solution and is subtracted from the target amount, nitrate included, one of the forms of nitrogen. Waterworks report nitrate as the whole ion, while target ranges mean the nitrogen inside it: 40 mg/L nitrate in tap water works out at 9.0 mg/L nitrogen, about 6 % of the 160 mg/L that one of the nitrogen trials found to be optimal. The German drinking-water limit of 50 mg/L also refers to nitrate; as nitrogen that is 11.3 mg/L. Sodium and chloride limit how suitable the water is. They are measured in millimoles per litre, a quantity counted by number of particles: below 1.5 mmol/L, which is 34.5 mg/L sodium or 53.2 mg/L chloride, water counts as suitable for all greenhouse crops, and up to 2.5 mmol/L still for crops whose solution is not recirculated.

Water hardness follows from calcium and magnesium: one degree of German hardness, 1 °dH, corresponds to 7.15 mg/L calcium or 4.33 mg/L magnesium. Acidifying depends on a different value, the acid capacity KS4.3. It states how much acid one litre of water takes up before it reaches pH 4.3, and so measures mainly the bicarbonate, the substance in the water that absorbs added acid. A widely used working formula sets bicarbonate equal to KS4.3 minus 0.05 mmol/L; 1 mmol/L of it corresponds to 2.804 °dH of carbonate hardness. In substrate growing the bicarbonate is neutralised with acid until 0.5 to 0.75 mmol/L remain, and the amount of acid follows the bicarbonate itself. The acid brings a nutrient of its own into the solution: per millimole of neutralised bicarbonate, nitric acid delivers 14.01 mg nitrogen as nitrate, phosphoric acid 30.97 mg phosphorus and sulphuric acid 16.03 mg sulphur. Acidifying water with 2 mmol/L bicarbonate down to 0.5 mmol/L with phosphoric acid therefore works out at around 46 mg/L phosphorus, more than the whole range of 11 to 25 mg/L above which phosphorus brought no further benefit in peat. Anyone mixing tap water with rainwater or reverse-osmosis water, water from which a membrane has removed most of the salts, lowers all of these values in proportion to the mix.

Bunkerlinge fertiliser calculator

The calculator shows how many milligrams of each nutrient a mix of commercial fertilisers delivers per litre of water, includes the irrigation water and sets the result next to the ranges from cannabis studies.

What the target ranges were measured on

The target values in the nutrient calculator refer to the solution as it is mixed: in the watering can, in the tank or at the dripper. What sits in the pot or the tank later can look very different. Whatever the plant does not take up stays behind in the pot until it runs out of the bottom with the irrigation water. That run-off is called drain, and the less of it there is, the more salt builds up in the pot.

Two trials show how far this can go. In peat, with 15 % of the irrigation water running out of the bottom, the phosphorus feed was tripled, and phosphorus in the drain rose twelvefold. In a closed hydroponic system, spent solution was only topped up. The top-up carried 90 mg/L phosphorus, yet the tank held around 300 mg/L, more than three times as much. Anyone who mixes exactly to the target and then waters so sparingly that hardly anything runs off, or only tops up the tank, can therefore have a multiple of what the calculator shows at the roots.

The ranges themselves come from pot and bucket trials with one or two varieties per study. The plants grew in perlite, a fired volcanic rock that holds hardly any nutrients, in peat mixes or in hydroponics, where the roots hang in the solution. Potassium shows how differently two varieties can behave: in one trial with two varieties, one grew best at 175 mg/L, while the other grew no better above 60 mg/L, even when it got more. Whether another variety resembles the one, the other or neither has not been studied for cannabis. The ranges are therefore a starting point to be checked on the plant itself, for example with a leaf analysis as described further down.

Nitrogen: amount and form

In the vegetative phase, the growth before flowering, 160 mg/L nitrogen was optimal in a perlite trial with one variety; at 240 mg/L root growth was already held back, and there was no measurement between the two levels. A hydroponic study with another variety recommends 160 to 200 mg/L. In flowering, yield reached a plateau at around 160 mg/L in two substrate trials: one CBD variety produced 16.1 g of dry flower per plant at 80 mg/L, 22.6 g at 160 and 26.3 g at 240 mg/L, yet CBD yield per plant was statistically the same at 160 and 240 mg/L. A hydroponic model places its optimum at 194 mg/L. More nitrogen lowered the concentration of cannabinoids, the active compounds such as THC and CBD, in the two substrate trials, and in a trial with misted roots the THC content of two varieties fell by 9.5 % when 250 instead of 150 ppm was given; in the hydroponic model nitrogen had no effect on them. Growing for potency rather than yield therefore means staying at the lower end.

Plants take up nitrogen as nitrate and as ammonium, two different ions. In a perlite trial with one variety, at a constant 200 mg/L nitrogen, pure nitrate did best: as little as 10 % ammonium in the total nitrogen cost 35 % of flower yield, 50 % cost 46 %, and at 100 % only 3 % of the yield was left. The authors consider up to 30 % ammonium acceptable and advise against more; the 30 % is therefore stated as an upper limit. A contrary study that found better cannabinoid values at 40 % ammonium rests on three plants per level and unclear statistics. Urea, a nitrogen compound that is first converted to ammonium in the root zone, was not used in any of the cannabis studies read.

Phosphorus, potassium, magnesium and the other elements

For phosphorus in flowering the findings depend on the system, and they cannot be averaged into one value. In perlite with around 30 % drain the yield plateau ran from 30 to 90 mg/L; 90 mg/L was simply the highest level tested. In peat, phosphorus above 11 to 25 mg/L added neither yield nor cannabinoids. In hydroponics two studies contradict each other: in a closed system 15 mg/L was enough, while in buckets with weekly solution changes a model placed the yield optimum at around 59 mg/L. For the vegetative phase no substrate trial has been read. In flowering, potassium between 60 and 175 mg/L made no difference to yield, but the acid forms of the cannabinoids and the terpenes, the plant’s aroma compounds, fell as potassium rose, and 240 mg/L harmed one of two varieties; the authors suggest 60 mg/L. Magnesium had its optimum in flowering at 35 mg/L in a drug-type variety grown in perlite, while two CBD hemp varieties in peat and perlite grew best at 50 to 75 mg/L.

For calcium, sulphur, boron, copper, iron, manganese and molybdenum none of the cannabis studies read tested graded concentrations. What the trials had of them in the solution came from a constant base solution, in one of the nitrogen trials a calculated 44.9 mg/L calcium and 88.8 mg/L sulphur. That these elements are needed is shown by omission trials, in which one element at a time was left out: without sulphur, flower yield of one variety in hydroponics fell by 34 %; without calcium the cannabinoid levels were the lowest, although the calcium-free solution also held the most sodium; and in young hemp plants without boron or without copper, dry mass fell by 28 % and 45 %. Such a trial does not say how much is optimal. For zinc, 0.35 mg/L was optimal in flowering, in one study. The leaf remains the check: ranges for tissue content come from 6119 hemp samples, for boron about 30 to 90 ppm, and a leaf analysis shows what the plant has taken up, whereas the calculation only says what was on offer.