Hydroponics Systems: Using the Two Basic Equations to Calculate a Nutrient Solution Recipe

If you are unfamiliar with the two basic equations, read this first: Hydroponic Systems: Calculating Nutrient Solution Concentrations Using the Two Basic Equations.

Here is our problem: We want to use a Modified Sonneveld Solution (Mattson and Peters, Insidegrower) for herbs in an NFT system. We will be using two, 5-gallon stock tanks and injectors set to a concentration of 100:1, call them Stock tank A and Stock tank B. How much of each fertilizer do we need to add to each stock tank?

The first thing to notice is we have three sources for providing nitrogen (calcium nitrate, ammonium nitrate, and potassium nitrate), two sources for providing potassium (potassium nitrate and potassium phosphate monobasic), and one sources for providing calcium (calcium nitrate) and phosphorus (potassium phosphate monobasic). We can start calculating the calcium or phosphorus in the recipe because only one fertilizer provides each nutrient. Let's start with calcium.

The recipe calls for 90 ppm calcium. We'll calculate how much calcium nitrate we need to use to provide this using the first of our two basic equations.

We need to add 895.3 g of calcium nitrate to supply 90 ppm calcium. However, calcium nitrate also contains nitrogen. We'll use the second equation to determine how much nitrogen will be supplied in ppm.

We are adding 73.4 mg N/l or 73.4 ppm of nitrogen. Our recipe calls for 150 ppm of nitrogen. If we subtract 73.4 ppm nitrogen from this, we see that we still need to add 76.6 ppm nitrogen.

Let's calculate how much potassium phosphate monobasic we need to use to supply 31 ppm phosphorus.

We need to add 262 g of potassium phosphate monobasic to supply 31 ppm phosphorus. However, potassium phosphate monobasic also contains potassium. We'll use the second equation to determine how much potassium will be supplied in ppm.

We are adding 39 mg K/l or 39 ppm of potassium. Our recipe calls for 210 ppm of potassium. If we subtract 39 ppm potassium from this, we see that we still need to add 171 ppm potassium.

We only have one other source for potassium, potassium nitrate. Let's calculate how much we need to use.

We need to add 885 g of potassium nitrate to supply 171 ppm potassium. However, potassium nitrate also contains nitrogen. We'll use the second equation to determine how much nitrogen will be supplied in ppm.

We are adding 61 mg N/l or 61 ppm of nitrogen. Our recipe calls for 150 ppm of nitrogen. We supplied 73.4 ppm nitrogen from calcium nitrate and still needed to add 76.6 ppm nitrogen. Now we can subtract 61 ppm nitrogen. We still need to add 15.6 ppm nitrogen. The only nitrogen source we have left is ammonium nitrate.

Let's calculate how much ammonium nitrate we need to use to supply 15.6 ppm nitrogen.

We need to add 86.7 g of ammonium nitrate to supply 15.6 ppm nitrogen.

At this point, we have completed the nitrogen, phosphorus, potassium, and calcium part of the recipe. For the remaining nutrients we only need to use the first equation because fertilizers we are using to supply them only have one nutrient in the recipe.

We need to add 498.5 grams of magnesium sulfate to provide 24 ppm magnesium.

We need to add 18.9 grams of sequestrene 330 to provide 1 ppm iron.

We need to add 1.5 grams of manganese sulfate to provide 0.25 ppm manganese.

It is easier to weigh small amounts of fertilizers in milligrams. So, the conversion from milligrams to grams is taken out of the following.

We need to add 692 milligrams of zinc sulfate to provide 0.13 ppm zinc.

We need to add 0.17 milligrams of copper sulfate to provide 0.023 ppm copper.

We need to add 2.8 milligrams of borax to provide 0.16 ppm boron.

We need to add 0.12 milligrams of sodium molybdate to provide 0.024 ppm molybdenum.

Now all the calculations are complete. We need to decide which stock tank, A or B, to put each of the fertilizers in. In general, we want to keep the calcium in a different tank than the sulfates and phosphates because they can form precipitates that can clog drip emitters in the irrigation system. Using this guideline, we can put the calcium nitrate in one tank and the potassium phosphate monobasic, magnesium sulfate, manganese sulfate, zinc sulfate, and copper sulfate in the other tank. The rest of the fertilizers can go in either tank.

You should also consider the amounts of nutrients in the irrigation water. For example, if we are using irrigation water that contains 10 ppm of magnesium, we only need to add 14 more ppm (24 ppm Mg called for in the recipe minus 10 ppm Mg in the water) with our fertilizer. This is a great way to more efficiently use nutrients and fine-tune your fertility plan.

For some micronutrients, it's up to you to decide what to add. You might consider conducting a small experiment to see if you need to add 0.12 milligrams of sodium molybdate, for example, to your stock solution or if you are satisfied with the performance of your plants without it.

One last thing to consider. Sometimes the calculations do not work out as nicely as they did here for fertilizers containing more than one needed nutrient, and you may need to add more of a nutrient than a recipe calls for in order to supply the other nutrient.

For example, you may find that when you apply calcium nitrate to meet calcium needs, the solution does not contain enough nitrogen. In cases like these, you'll need to decide which nutrient to prioritize. For example, you could apply calcium nitrate to meet the plant's nitrogen needs because the amount of calcium in excess will not harm the plants. Or, you may decide to apply it based on the plant's calcium needs because the amount of nitrogen lacking is only a few ppm.