First Horticultural Math Exercise, bucket chemistry 1

First horticulture math problems.
show all work :slight_smile: @mastergrowers

I want to compare the cost of my nitrogen source in my fertilizer. Same math for other elements.



What is the cost of pure nitrogen per pound of each formulation?

Which fertilizer cost the least?

You can do the same calculation for N-P-K.

The formulation of the peters Cal Mag is

Total Nitrogen (N)… 15%
1.1% Ammoniacal Nitrogen
11.8% Nitrate Nitrogen
2.1% Urea Nitrogen
Available Phosphate (P2O5)… 5%
Soluble Potash (K2O)… 15%
Calcium (Ca)… 5%
Magnesium (Mg)… 2%
2% Water Soluble Magnesium (Mg)
Boron (B)… 0.0187%
Copper (Cu)… 0.0187%
0.0187% Chelated Copper (Cu)
Iron (Fe)… 0.075%
0.075% Chelated Iron (Fe)
Manganese (Mn)… 0.0375%
0.0375% Chelated Manganese (Mn)
Molybdenum (Mo)… 0.0075%
Zinc (Zn)… 0.0375%
0.0375% Water Soluble Zinc (Zn)

The formulation of peters acid special

Total Nitrogen (N)… 21%
10.4% Ammoniacal Nitrogen

10.6% Urea Nitrogen||
|Available Phosphate (P2O5)…||7%|
|Soluble Potash (K2O)…||7%|
|Magnesium (Mg)…||0.6%|
||0.6% Water Soluble Magnesium (Mg)||
|Sulfur (S)…||13%|
||13% Combined Sulfur(S)||
|Boron (B)…||0.0262%|
|Copper (Cu)…||0.0262%|
||0.0262% Chelated Copper (Cu)||
|Iron (Fe)…||0.15%|
||0.15% Chelated Iron (Fe)||
|Manganese (Mn)…||0.05%|
||0.05% Chelated Manganese (Mn)||
|Molybdenum (Mo)…||0.01%|
|Zinc (Zn)…||0.05%|
||0.05% Chelated Zinc (Zn)||

Extra credit do the same calculation on

Peters 15-16-17 Peat-Lite. $42 for a 25# bag.

What is the percentage by weight of each form of nitrogen?

Additional credit what is the minimum soil temperature for conversion of urea to nitrate? Not really a math problem but a grower problem.


Calculate 400 ppm of nitrogen for each of the above products. 1 to 1 ratio to start with.

What is the most cost effective source of nitrate from the above fertilizers.

Extra credit, what is the maximum solubility of the concentration for each formulation. This is tricky.

Extra, extra credit. For field production only what is cost per pound of nitrogen for your local formulation of Ag grade balanced fertilizer eg. 1-1-1, 13-13-13 or 19-19-19. Each local will have its own Ag grade balanced fertilizer. And the cost varies dramatically across the country by location.

@Growernick @nick and @Hunter do we have GN swag for the winner?

Last call will close and provide answer next week Friday December 21 at 7 PM PSDT


One more extra credit problem pick any organic fertilizers with a legal analysis and tell me the cost of the nitrogen and the formulation of the nitrogen.

Our friends at Growers House will be a useful source for the calculation.


I can make the swag happen.


@Nate Think anybody would like to hop in on a little math exercise?


I will supply the simplified math at the close of submissions. The math is so simple you can do it on a napkin.

Who will the judge be?


I’ll take a stab at it.

15-5-15 costs $12.80/N#
21-7-7 costs $8.19/N#

Is this a trick question? As a total of N+P+K, the 15-15-15 is chepaer @ $4.27/NPK#, while the 21-7-7 is $5.25/NPK#. On a purely nitrogen based cost analysis, the 21-7-7 is cheaper as shown above.

400ppm of 15-15-15 is 2.66g/L
400ppm of 21-7-7 is 1.91g/L

21-7-7 is most cost effective for N only.

I believe total maximum solubility of the formulation is going to be based on the least soluble ingredient. Temperature and pH will determine maximum solubility, so I will say, “not enough information”. :wink:

Personally, I use 46-0-0 ($19/50#), 16-16-16 ($12/50#), and 22-0-22 ($19/50#) and work out my needs based on soil tests.

I choose to compare mined sodium nitrate (technically organic) and blood meal.

Nitrate: 15-0-2 @ $34.00 for 50lbs
Cost: $4.50/N#

Blood Meal: 12-0-0 @ $84.76 for 50lbs
Cost: $14.13/N#

For comparison of just nitrogen and its cheapest source:

Urea: 46-0-0 @ $18.99 for 50lbs
Cost $0.83/N#


Show your work.


My favorite local nutrient mathematician is @mike.c1. Maybe he’s willing to take a stab at it :wink:


Yes and know. For ever soluble fertilizer ther is a max solubility number. It is based on a pH of 7. And yes it is the least soluble chemical, but it is affected by the other ingredients in the formulation you are using.

As for cost for nitrogen show your work your almost there.

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How about a formula?

Cost per #N
$ / (Percent N (decimal) * bag weight in lbs) = $/N#

PPM (g/L)
Desired ppm / percent N (decimal) / 1000 (g/L water) = g of formula per L

Max Sol:
15-15-15: 3lbs per gallon
21-7-7: 40lbs per gallon
(Note: I cheated, it’s on the label)


Close but you need to correct for the molecular weight of each form of nitrogen. You maybe in for a shock as the price of N will change.

It’s not cheating to read labels. One of my wife’s jobs on the farm was making sure a copy of each label was in our handling book. Plus every MSDS sheet you can imagine. Light bulbs to toilet paper. The hand soap in our bathroom.


Does source matter on a label? Isn’t the %N the available N so it is already accounted for?


Yes they cheat. It is an open secret in agriculture. They use the percentage of the form of nitrogen not actually nitrogen. It is a hold over from the old days. It is not true of P or K. But is an issue for Ca.


I’ll have to look into that one more, news to me. I thought the percent N on a label, was actual N, not by molecular weight. That’ll have to be later, bank compliance officer should be here anytime now, and I’m using math as an excuse not to keep cloning my house. :rofl:


ammoniacal nitrogen molecular weight


or if you prefer H3N or 82.245 % nitrogen

34.062 g/mol

Nitrate NO3 only 26% Nitrogen

62 grams per mole

Urea 60.056 g/mol CH4N2O 47 % Nitrogen.



Isn’t it an issue for everything on the guaranteed analysis? You’re getting 5% P2O5, NOT 5% P and 15% K2O, NOT 15% K. Isn’t that the case for all of the ions listed on the analysis?

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Yes you are correct but, when it comes to nitrogen. Money becomes an issue

Potassium, and phosphorus just don’t cost what nitrogen does. So as farmers we get screwed on our formulation of nitrogen. I want nitrate, because of all the associated cost to urea and ammonia.

Calcium is so inexpensive that formulation does not add much to your cost accounting.

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Let me add to this. What are we trying to pay for? If you look at a liquid fertilizer, like fish emulsion. It has an garenteed analysis of 5-2-2. I am paying most of my money for very expensive water.



Very cool. i do know the answers. However i want to watch. ill toss in a pack of beans for the winner aswell.


This is why i try to make mostly my own mix. takes more time. but i dont like double buying my water.