How to calculate nutrient solution formulas

A nutrient solution is the mix of irrigation water with added nutrients. It is mainly used in soilless culture and hydroponics, where the nutrient solution is the only source of nutrients to the plants.

Calculating and balancing the nutrient solution formula might be confusing. Following the proper steps is the best way to avoid mistakes.  These steps are:

The source water may contain essential nutrients, which must be accounted for. Therefore, it is important to test the irrigation water before calculating the fertilizers to be added to the nutrient solution.

Note that the lab may provide the test results in different units, such as ppm, mg/l, meq/l, mmol/l.

To simplify the calculation, it is recommended to convert all values to ppm. A conversion table is available here.

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Determine the nutrient rates your crop requires. You can use recommendations from the literature, or

your own experience.

If nutrient requirements are provided in units other than ppm or mg/l, it is recommended to convert

the values to ppm (1ppm = 1 mg/l).

To do so, simply deduct the source water test results from the nutrient requirements of the crop. Repeat that for each nutrient.

For example, if magnesium requirement is 60 ppm and the source water contains 40 ppm, then 60-40=20 ppm of magnesium has to be added with fertilizers. This means 20 milligrams of magnesium have to be added to each liter of nutrient solution.

A negative value means your source water contains more of the nutrient than the crop needs and, therefore, you should not use fertilizers that contain that nutrient.

The  fertilizer you select must contain all nutrients that need to be added, as per the calculation in step 3.

Check which fertilizers you have available that contain those nutrients.

Begin with the fertilizer that contains a unique nutrient, that other fertilizers do not contain. For example, if the only available source of calcium you have is calcium nitrate, start the calculation with this fertilizer.

For solid fertilizers:

FR = 100 x NA / %N

Where

FR is the fertilizer rate to apply in ppm (or mg/l).

NA is the required nutrient concentration to be added by this fertilizer in ppm (1 ppm = mg/l = 1 g/m³).

N is the concentration of the nutrient in the fertilizer.

For liquid fertilizers:

FR = NA / (% N x D x 10)

Where D is the density of the fertilizer in kg/L and FR is the fertilizer rate in of ml/L or L/m³.

And when the density of the fertilizer (D) is given in lbs/gallon, the formula becomes:

FR = NA / (%N x D x 11.98)

Where FR is the required application rate in gal/1000gal.

The percent nutrients that a fertilizer contains is usually given as a percent weight to weight and, therefore, dividing by the density of the fertilizer is required.

Now, you have to find the right combination of fertilizers that balances all the required nutrients.

Since for some nutrients you may have to use multiple fertilizer sources, it is recommended to prepare an Excel table that includes the fertilizers to be used and the rate of nutrients each of them contributes.

1. The concentration of the nutrient in the fertilizer may be given in the oxide form. Pay attention for which form you do the calculation. For example, MAP 0-52-34 contains 52% K2O and 34% P2O5. To calculate the rate of the fertilizer required to apply certain concentrations of K and P, you should first convert % K2O and P2O5 % of K and P.52% P2O5 = 22.7% P
   38% K2O = 31.6% K
   Click here to view a conversion table

2. Nitrogen may be applied in two different forms – nitrate (NO₃^–) and ammonium (NH₄⁺). The ratio between these two forms is of a great importance in nutrient solutions. Therefore, you may want to break down the nitrogen calculation to these two forms. For example, MAP (mono ammonium phosphate) contains 12% N-NH4, while potassium nitrate contains 13% N-NO₃. This means the nitrogen in MAP is in its ammonium form, while in potassium nitrate it is in the nitrate form. Some fertilizers may contain both forms.

3. Often, the pH of the nutrient solution has to be lowered. This is done by adding acid to the nutrient solution. The three most common acids are nitric acid, phosphoric acid and sulfuric acid. As can be suggested from their names, those acids contribute nutrients to the nutrient solution. Nitric acid contributes nitrogen, phosphoric acid – phosphorus and sulfuric acid – sulfur. These nutrients must be accounted for when doing the calculation.

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