Rather than address your question directly I have some suggestions:

• if you are growing crop plants to an advanced stage the soil depth typically needs to be need to be at last 30 cm to get normal growth;
• you should seriously consider expressing concentrations as the elements in mg/kg rather than kg/ha. This is the standard for publication because expression as the oxides is entirely artificial, and the process of mixing and potting soil changes the bulk density from what it was in the field.

Best wishes, Paul.

I assume that the fertilizer recommendations are linked to the 75,000 plants / ha density. In this case, it might make sense to simply calculate the fertilizer recommendation on a "per-plant" basis. This would follow the recommendation. And given that you know the weight of the soil in the pot, you can express this as mg / kg soil, as well as mg / plant. As Paul Milham mentioned, be careful about the difference between expressing fertilizer amounts expressed as P2O5 and P.

Thank you @ Paul Milham and @ Sal Mangiafico for your suggestion. I guess I have to place more emphasis on soil depth in the pot rather than the weight. The fertilizer recommendation are linked to the 75,000 plants/ha.

You will have fewer plants in deeper pots but the number/ha will remain high because the surface area of each pot will be smaller.

Please also consider how genetically variable the plants may be and therefore how many plants you may need to have reasonable stats. That will also impact the number of replicates. I general it's good practice to have a minimum of 6 reps, properly laid out in randomised blocks in a space that is as uniform as possible. Any restrictions on design should be discussed with a biometrician during the planning.

The usual practice to reduce variation is to pre-germinate the seed and sow many more uniform seedlings in each pot than you want to grow to maturity. After a couple of weeks reduce the number to a uniform population at the density you plan to continue with.

Depending on the treatments please consider making measurements on these thinnings as insurance against a problem later in the experiment.

Such experiments require attention every day.

It is a good idea @Sal-Mangiafico to follow per plant as the recommendation is for 75000 plants/ha. But, you have to take care of volume of soil in the pot.

For the pot experiment, you can calculate the fertilizer requirements based on the amount of soil you want to add.

I'm not always comfortable with doing such calculations based on the expected number of plants per hectare because pot trials often do not have a provision for adopting a given plant spacing to correspond to the expected number of plants in a hectare. In most cases, pot trials involve one plant per pot regardless of pot size. Also, the rooting depth of the crop may not be important because no one does pot trials with the aim of growing the crop to maturity and achieve similar yields as in the fields. For these reasons, pot size and hence capacity translating into the amount of soil it could contain appears more reasonable.

On the above premises, I recommend you calculate the actual amount of each fertilizer to use based on the amount of soil in the pot. To do this, first calculate the amount (mass) of soil in a hectare to a depth about the same as the depth of the pots you intend to use as mass = soil bulk density x volume of soil, whereby the latter is area of hectare (10000 sq. m) x soil depth in m. With this and the application rates of the fertilizers already known, a simple extrapolation would be used to get the equivalent amount of fertilizers to add to your potted soils.

To calculate the fertilizer requirement for a pot experiment with NPK 15-5-30, you need to first convert the recommended nutrient application rates from per hectare (ha) to per unit area of your pot. The following steps will guide you through the calculations:

Step 1: Determine the size of your pot in square meters (m²). For example, if the pot has a diameter of 50 cm and a height of 40 cm, the surface area can be calculated as: Surface area = π x r² + 2πrh Surface area = 3.14 x 0.25² + 2 x 3.14 x 0.25 x 0.4 Surface area = 0.196 + 0.502 Surface area = 0.698 m²

Step 2: Calculate the recommended nutrient application rates per unit area of the pot. To do this, divide the recommended nutrient application rates by the area of the pot:

• Nitrogen (N): 240 kg/ha ÷ 10,000 m²/ha = 0.024 kg/m²
• Phosphorus (P2O5): 91.61 kg/ha ÷ 10,000 m²/ha = 0.009161 kg/m²
• Potassium (K2O): 385.47 kg/ha ÷ 10,000 m²/ha = 0.038547 kg/m²

Step 3: Calculate the amount of fertilizer required. To do this, you need to know the percentage of N, P2O5, and K2O in the fertilizer you are using. Let's assume you are using a fertilizer with the same NPK ratio (15-5-30) as the recommended rates.

• Nitrogen (N): Divide the recommended amount of N per unit area (0.024 kg/m²) by the percentage of N in the fertilizer (15%) and multiply by 100 to convert from kg to grams. Fertilizer required = 0.024 kg/m² ÷ 0.15 x 100 = 16 g
• Phosphorus (P2O5): Divide the recommended amount of P2O5 per unit area (0.009161 kg/m²) by the percentage of P2O5 in the fertilizer (5%) and multiply by 100 to convert from kg to grams. Fertilizer required = 0.009161 kg/m² ÷ 0.05 x 100 = 18.32 g
• Potassium (K2O): Divide the recommended amount of K2O per unit area (0.038547 kg/m²) by the percentage of K2O in the fertilizer (30%) and multiply by 100 to convert from kg to grams. Fertilizer required = 0.038547 kg/m² ÷ 0.30 x 100 = 12.85 g

So, for each pot with a surface area of 0.698 m², you would need to apply 16 g of NPK 15-5-30 fertilizer, of which 2.4 g would be nitrogen, 0.916 g would be phosphorus, and 1.285 g would be potassium.