How do I convert a formula in ppm to amounts of individual fertilisers?

I have received several successfully proved formulas for the crops I grow, however they are expressed as ppm (parts per million) of the various nutrient ions. How to do convert these to the practical amounts of fertiliser to use?

Answer by RICK DONNAN

Formulations and solution analyses are usually expressed as parts per million. A numerically equal alternative unit is milligrams/litre (1 mg is 1/1000 g and 1 litre of water is 1000 g, hence 1 mg/l =1/1000 x1000 = 1/1000,000 = 1 ppm). In many countries molar units are used, but I’ll ignore these for this question.

Fertiliser analyses
To work out how much of each individual fertiliser to use you need to know the nutrient analysis of that fertiliser. It is essential to take this from the bag of fertiliser that you are using. Most greeenhouse grade fertilisers will print the percentage of each nutrient component on the bag. It is vital to use these figures and not just take the figures given in text books or articles. These are often taken from chemistry handbooks for the pure chemicals of the same name. The actual percentages can be quite different, especially in the case of calcium nitrate (pure calcium nitrate contains 16.9% Ca and 11.9% NO3, whereas typical greenhouse grades contain 19.0%Ca, 14.4% NO3 and 1.1% NH4.)

Calculation basis
For these calculations I’ll work on dissolving grams of fertiliser to give 1000 litres (1 kL) of standard nutrient solution. In this case, each gram is equivalent to 1 ppm (1gram / kilolitre = 1g /1000 x 1000 gram water = 1 ppm).

For example, say a fertiliser contains 15% of nutrient ‘A’.
If the formulation is to contain 60 ppm of ‘A’, this requires 60 g of ‘A’ in the fertiliser.
At 15% A, this needs 60 x 100 / 15 = 400 g actual fertiliser.
Fertiliser required = 400g (per kL of solution).

Formulation example
For this answer, let’s take a hypothetical formulation as follows:
180ppm Ca, 200 ppm N as NO3, 18 ppm N as NH4, 320 ppm K, 50ppm P, 60ppm Mg, 130ppm S as SO4.

Calculation sequence
Fertilisers typically contain not just one nutrient, but always two or sometimes more, as in the case of calcium nitrate. You need to work through a sequence that allows for nutrients often being supplied in more than one fertiliser. It is easiest to start calculations considering a nutrient which comes in only one fertiliser, such as the only source of calcium is calcium nitrate. This calculation gives grams fertiliser to dissolve in 1000 litres at normal feed strength.

Calcium nitrate
Start with calcium nitrate typically containing 19% Ca, 14.4% N as NO3, 1.1% N as NH4
Calcium nitrate needed = (ppm Ca needed) / (% Ca in fertiliser) = 180 x 100/19 = 947 g
The calcium nitrate also brings NH4 containing = 947 x 1.1 / 100 = 10 ppm N
leaving NH4 still needed = 18 – 10 = 8 ppm N
Calcium nitrate also brings NO3 containing = 947 x 14.4 / 100 = 136 ppm N
leaving NO3 still needed = 200 – 136 = 64 ppm N.

Ammonium nitrate
Get NH4 from ammonium nitrate typically containing 17.5% N as NH4, 17.5 % N as NO3
Ammonium nitrate needed = 8 x 100 / 17.5 = 46 g solid, or 92 ml 50% solution
The ammonium nitrate also brings NO3 containing 46 x 17.5 / 100 = 8 ppm N
Leaving NO3 still needed = 64 – 8 = 56 ppm N.

Potassium nitrate
Get NO3 from potassium nitrate typically containing 13% N as NO3, 38% K
Potassium nitrate needed = 56 x 100 / 13 = 431 g
Potassium nitrate also brings K containing = 431 x 38 / 100 = 164 ppm K
Leaving K still needed = 320 – 164 = 156 ppm K.

Mono potassium phosphate (MKP)
Get P (50 ppm) from mono potassium phosphate (MKP) containing 23% P, 28% K
MKP needed = 50 x 100 / 23 = 217 g
MKP also brings K containing = 217 x 28 / 100 = 61 ppm K
Leaving K still needed = 156 – 61 = 95 ppm K.

Potassium sulphate
Get the remaining K from potassium sulphate containing 18% S, 45% K
Potassium sulphate needed = 95 x 100 / 45 = 211 g
This brings with it = 211 x 18 / 100 = 38 ppm S.

Magnesium sulphate
Get magnesium (60 ppm) from magnesium sulphate containing 10% Mg, 13% S
Magnesium sulphate needed = 60 x 100 / 10 = 600 g
This brings with it = 600 x 13 / 100 = 78 ppm S
Gives total sulphur = 38 + 78 = 116 ppm S compared to the formulation of 130 ppm.

As sulphur is the macronutrient with the most flexibility, it is usually OK to use the sulphur content to balance the formulation.

Note that I have not included micronutrients (trace elements) as the calculations are identical.

Concentrated solutions
This calculation was for a working strength solution. For a 100 to 1 concentrate, multiply by 100.

To prevent precipitation in concentrated solutions, Ca (and Fe) ions must be kept separate from the P and S ions, otherwise these will have precipitation of calcium phosphate and calcium sulphate. Note that these compounds are totally soluble at working strength. A rough analogy in that it is easy to dissolve one teaspoon of sugar in a cup of tea, but impossible to dissolve 100 teaspoons of sugar.

Consequently, Part ‘A’ concentrate contains the calcium nitrate and iron chelate, and Part “B’ contains everything else.This gives more fertiliser in ‘B’ than in ‘A’, so even up the concentrations 1/3 to ½ of the potassium nitrate plus any ammonium nitrate is often added to part ‘A’.

“Successful” formulation warning
Your reference to ”successfully proved formulas“ leads me to introduce a note of caution. By far the most important aspect of hydroponic nutrition management is managing the solution around the root zone. This will always be different to your feed solution. The feed solution is most important as to the impact it has on the root zone solution, rather than being a ‘magic’ feed formula. There is also a significant impact as to whether you recirculate or not. If a slight nutrient imbalance develops in a free drainage system it is gone before any damage is done, however, if recirculating the buildup in imbalance can lead to problems.  Ω

PH&G August 2016 / Issue 170


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