Converting between concentrations: NPK percent, mg/L and ppm.

Descriptions of liquid fertilizers often mention the concentration. This could be as milligrams per liter (mg/L) or parts per million (ppm). It could also be indirectly expressed as percent mass (% or NPK). Thankfully, converting from one to another is a simple process. For a more detailed explanation of what these measurements mean and how to convert between them, read on.

Let’s review a few concepts first. These definitions were taken from dictionary.com

Mass: The quantity of matter as determined from its weight or from Newtons’ second law.
Volume: The amount of space, measured in cubic units, that an object or substance occupies.
Concentration: Measure of the amount of dissolved substance contained per unit of volume.

Simply, mass is something measured with a scale or balance. Volume is determined using a container, such as a beaker or graduated cylinder. Dissolving a known mass of a substance into a known volume of water allows one to calculate the concentration of the solution. Imagine we dissolved 5.0 grams of sugar into a two liter bottle of water:

5.0 grams sugar ÷ 2 liters water = 2.5 grams sugar/liter water

Solutions relevant to horticulture will not always be described as grams per liter. Depending if you are reading a research article in the Journal of Plant Nutrition, looking at a bottle of Miracle-Gro or following directions from an agricultural extension, the units indicated could vary. You will often find percent of total mass, mg/L or ppm mentioned. Other possibilities exist, such as teaspoons per gallon. However, if you understand the principles here, you can convert to and from those units as well.

Something important to remember:
One liter of pure water has one kilogram of mass!

PPM and mg/L
Both mg/L and ppm are concentrations. Converting between them couldn’t be simpler; they are effectively the same. Since a liter of pure water has the mass of one kilogram, where one kilogram is 1,000 grams, with each individual gram consisting of 1,000 milligrams, there are a million milligrams in a liter of water. This means that 500 mg/L is the same as 500 ppm. It would also be true that 1 g/L is equivalent to 1,000 ppm.

Percent mass and NPK
When you see the NPK numbers on a liquid fertilizer or nutrient bottle, those are given as a percent of the product’s mass, per unit volume. This should also be the case with any nutrient, macro or micro, listed on the guaranteed analysis. These numbers are not the same as concentration. Converting between a mass and a concentration is analogous to converting between distance and speed. If we want to determine concentration from these numbers, we need to know two things; the volume and mass of the solution. Both should be listed somewhere on the product labeling. If not, the density can be measured with a hygrometer. Let’s examine the label for General Hydroponic’s Flora Micro one quart bottle. The full label can be viewed at the manufacturer’s website, by clicking here.

GH Flora Micro. Net weight 1.18kg. 946 ml

This one quart bottle has a volume of 0.946 L and a net weight of 1.18 Kg. Not shown is the guaranteed analysis of 5% calcium. Recall that one liter of pure water has the mass of one kilogram. This product however, although less than a liter, has a mass greater than kilogram. Make no mistake, this additional density is due to the dissolved salts in solution. For the sake of convenience, convert 1.18 kg into 1,180 grams. Next, multiply the total mass, 1,180 grams, by the 5% calcium content.

1,180 g × 0.05 = 59.0 g Calcium

We have now determined that, according to the label, you have 59.0 grams of calcium among the 0.946 liters of water.  Since we have a mass for the calcium and a volume of the solution, finding the concentration will be easy. Just divide mass by the volume.

59.0 g ÷ 0.946 L =  62.4 g Calcium / L

There you have it! This product has a calcium concentration of 62.4 g/L. It would be equally valid to say that the calcium concentration is 62,400 mg/L or 62,400 ppm.

Converting a concentration to a percent is similar. Let’s imagine that scientists have reported a potentially new type of cloning solution. Being a gardener with initiative, you cannot wait the eight to ten years it will take for hydroponic companies to poach this research and bring an overpriced product to the market. You decide to make it yourself.

Following the directions of the researchers, you prepare one liter of this experimental cloning solution. You mix 45 g of the active ingredient and 100 g of inert ingredients into one liter of water.  We already know the concentration of the active ingredient, chemical X, is going to be 45 g/L. Helpful as that may be, how would we determine the percent mass of chemical X? Divide the mass of chemical X by the total mass of the solution, including Chemical X. This means 45 g Chemical X + 1000 g water + 100 g inert ingredients.

45 g Chemical X ÷ 1145 g Solution   =  0.087

Splendid! If chemical X was listed like other ingredients on the guaranteed analysis, it would be shown as 8.7 percent .

These examples hopefully provide readers with the information they need to begin solving their own calculations. Don’t allow yourself to become too frustrated. They definitely become easier with practice. In addition, don’t be afraid to ask for help.

References:

Nielsen, R.L., Fertilizer reckoning for the mathematically challenged.  Agronomy Department, Purdue University. Accessed December 14, 2010.
http://www.agry.purdue.edu/ext/corn/news/articles.02/Fert_Math-0326.html

Peters, John., Fertilizer grades and calculations. Soil Department, University of Wisconsin. Accessed December 14, 2010.
http://www.soils.wisc.edu/extension/materials/Fert_Grade_Calc.pdf

Reid, Keith. Is that fertilizer a good deal?  Ontario Ministry of Agriculture and Rural Affairs.  Accessed December 14, 2010.
http://www.omafra.gov.on.ca/english/crops/field/news/croptalk/2008/ct-1108a4.htm

Edited December 14, 2010 to include references and correct errors in NPK calculations.