Fertilizer Calculations: Understanding Parts per Million

While teaching greenhouse and nursery management classes, I have found that students often have the most trouble learning how to calculate fertilizer and plant growth regulator ratios. All of these are typically based on parts per million or ppm. Most fertilizer bags and PGR labels have all the calculations printed on them, but often a refresher on the calculations is in order.

Parts Per Million

The use of liquid feed fertilization programs in greenhouse and greenhouse crop production is the standard of our industry. Many growers use either a constant feed program fertilizing with each irrigation, while others use a pulse feed program fertilizing on a regular periodic schedule. The program selected is determined by crop requirements, available equipment, and personal preference. The most important concern, no matter which program is used, is accuracy in calculation of fertilizer concentrations.

Crop nutrition requirements and most published fertilizer schedules use the terminology "parts per million" or ppm. There are fertilizer tables provided by most fertilizer producers for easier reference. With a little knowledge, a calculator, and patience, the tables are not necessary.

Many growers are familiar with the Quick "75" Method for calculating ppm. To calculate the amount of fertilizer required, divide the desired ppm by 75 and then divide by the decimal fraction of the desired nutrient (such as nitrogen, potassium or phosphorous) contained in the fertilizer. This results in the number of ounces of fertilizer to use in 100 gallons of water.


To use this equation, assume that the fertilizer recommendation calls for 200 ]ppm of nitrogen from ammonium nitrate (33% N)-Using the above equation, divide 200 ppm by 75 resulting in 2.67,and then divide by 0.33. The answer is 8.09 ounces of ammonium nitrate which dissolved in 100 gallons of water will yield 200 ppm nitrogen.


Confused? Some examples of what one part per million represents under various conditions are: 1 crystal of salt in 5 lbs., 1 drop in 16 gallons, 1 inch in 158 miles, 1 minute in 1.9 years, 1 pound in 500 tons, and 1 cent in $10,000. Therefore, to calculate ppm in 100 gallons of water, first multiply 100 gallons by 8.34 pounds per gallon which equals 834 pounds. Multiply 834 pounds by 16 ounces per pound which equals 13,344 ounces per 100 gallons. Therefore, 13,344 ounces per 13,344,000,000 ounces equals 1 part per million, or more simply 0.013344 ounces per 100 gallons of water equals 1 PPM.

1. 100 gal. * 8.34 lbs./gal. = 834 lbs.


2. 834 lbs. * 16 oz/lb. = 13,344 oz.


3. 3,344 oz/100 gal.


4. 13,344 oz./13,344,000,000 oz. = 1 PPM


5. 0.013344 oz./100 gal. = 1 PPM
   
   

The next step is to multiply the desired PPM by 0.013344, which is 74.94. By rounding 74.94 to 75, it must by understood that the result will not be entirely nor mathematically accurate, but perhaps is close enough for practical purposes. Within the units of the ratios commonly used in fertilizer solution, the error will be 0.02 or less per 100 gallons.

For those who can think in metric terms, there is an easier way to calculate PPM By definition, 1 milliliter (ml) of water weighs 1 gram (g), therefore 1 liter (1000 ml) weighs 1000 g. Thus 1 liter (L) of water weighs 1,000,000 milligrams (mg). This tells us that 1 PPM equals 1 mg/1,000,000 mg of water or 1 mg/L of water. To calculate PPM in liters, simply multiply the desired PPM by 1 and divide by fraction of the fertilizer. This results in the number of mg of fertilizer to use in 1 L of water.


To illustrate this equation, use the same fertilizer recommendation as before, 200 PPM N from ammonium nitrate (33%N). Substituting in the above equation, multiply 200 by 1 resulting in 200, and then divide by 0.33. The answer is 606 mg of ammonium nitrate, which dissolved in 1 L of water will yield 200 PPM nitrogen.


To increase this to irrigation volumes, multiply this result by the required volume. Multiply 606 mg by 380 L (100 gal) which equals 230,280 mg or 0.507 pounds (8.12 oz).