Making a Fertilizer from Scratch

[Farmer Ray]

On fertilizer labels, NPK stands for the percentage by weight of the three primary macronutrients: Nitrogen, Phosphorus (as phosphate), and K potassium (as potash).

I'm currently using a product I like with N-P-K 4-5-13, but it is a little expensive and I would like to mix the three raw ingredients myself, but need to do so in the appropriate ratio. They each have a different N-P-K ratio.

The three raw ingredients are: Fish Protein Hydrolysate 12-1-1, Potassium Sulfate 0-0-50, Bone Meal 3-15-0

How much of each raw ingredient do I need achieve a N-P-K ratio of 4-5-13? If that ratio is not possible, then what ratio would be closest?

 

[joyfulerst]

On fertilizer labels, NPK stands for the percentage by weight of the three primary macronutrients: Nitrogen, Phosphorus (as phosphate), and K potassium (as potash).

I'm currently using a product I like with N-P-K 4-5-13, but it is a little expensive and I would like to mix the three raw ingredients myself, but need to do so in the appropriate ratio. They each have a different N-P-K ratio.

The three raw ingredients are: Fish Protein Hydrolysate 12-1-1, Potassium Sulfate 0-0-50, Bone Meal 3-15-0

How much of each raw ingredient do I need achieve a N-P-K ratio of 4-5-13? If that ratio is not possible, then what ratio would be closest? snow rider

You can treat this as a weighted-average problem, since the N-P-K numbers are just percent by weight.
Let x, y, z be the fractions of fish hydrolysate (12-1-1), potassium sulfate (0-0-50), and bone meal (3-15-0). You want their weighted average to be 4-5-13.
When you set up the equations and solve them, you quickly find there’s no solution with all three fractions ≥ 0 that hits 4-5-13 exactly. As soon as you balance nitrogen and phosphorus using the fish hydrolysate and bone meal, the potassium from the 0-0-50 source ends up far too high. In other words, potassium sulfate is so concentrated in K that it overshoots the 13% target before N and P can be matched.
So an exact 4-5-13 blend isn’t possible with these three ingredients. You can get close, but you’ll have to compromise on at least one nutrient (usually K ends up higher than 13), or switch to a potassium source with a lower K percentage.

 

[blamocur]

When you set up the equations and solve them, you quickly find there’s no solution with all three fractions ≥ 0 that hits 4-5-13 exactly

My equation yields 0.2542, 0.2549, 0.3164. I.e. if one mixes 0.2542 lb of Fish Protein with 0.2549 lb of Potassium Sulfate and 0.3164 lb of Bone Meal one will get about 0.8255 pounds of the mix which has the same amounts of N,P,K as 1 pound of the original fertilizer. One can add 0.1745 pounds of something neutral (sand?) to match the concentration, or simply adjust the amounts respectively.

 

[JeffM]

i get the same results as blamocur, but without the inert filler the concentrations will be too high.