Introduction
This guide will walk you through how-to calculate elemental PPMs in a nutrient mix.
Elemental PPMs are the weight ratio of each element in a nutrient solution to the overall weight of that solution, expressed as parts per million. This is not the same as TDS (Total Dissolved Solids) ppm, which is a measure of electrical conductivity converted to an equivalent number of Na (500-scale) or K (700-scale) ions in the solution.
There are several nutrient calculators available online, but this guide will walk you through the math and conversions if you want to do them yourself (e.g., as part of tracking your total feed amounts or comparing two product lines).
TL;DR
Elemental PPMs are just the concentration (by weight) of each element (N, P, K, etc) in your feed solution. The calculations are basically just unit conversions, but this guide walks you through the different units involved and the general math.
Their main use is for comparing feed schedules and mixes across vendors and product lines, as well as evaluating the relative impact of additives (e.g., cal-mag and pH adjusters) on your overall nutrient levels. They are also commonly used for reporting results in academic and scientific literature.
Step 1: Find Weight Percents for Each Product
Every fertilizer product is required by regulation to list “Guaranteed Minimum Analysis” nutrient levels on their labels (depending on their jurisdiction).
If you are calculating elemental PPMs for products you own, you can just check the labels. If you are considering purchasing a new product, you can check the manufacturers website for the information or try a google image search for the product label. In some cases, you can also try state or government agency databases for fertilizer products (e.g., the California Department of Food and Agriculture maintains a
searchable database of all fertilizer products registered for sale in the state).
Step 2: Convert to Element Weight Percents
When feed labels provide nutrient percentages in terms of molecular weight percent, these percentages need to be converted to elemental weight percents for each element of interest. Labels will typically list:
- Total N in addition to individual sources of N (e.g., ammoniacal, nitrate, urea, etc). Total N is the elemental weight percent and can be used directly.
- P and K percentages in terms of total phosphates and potash equivalent, respectively. These molecular weight percents need to be converted to elemental weight percents.
- Micronutrient percentages as elemental weight percents for each ion of interest. Occasionally, some labels will list a micronutrient in terms of its specific molecular form (e.g., SiO2). In these cases, the molecular weight percent will need to be converted to elemental weight percent.
In general, molecular weight percents can be converted to elemental weight percent by multiplying by the ratio of atomic weights:
- Elemental Weight Percent = Molecular Weight Percent * (Total atomic weight of element of interest / total molecular weight)
For example:
- 1% Phosphate (P2O5) = 1% x (2*30.97) / (2*30.97 + 5*16.00) = 0.44% Elemental P
- 1% Potash (K2O) = 1% x (2*39.10) / (2*39.10 + 16.00) = 0.83% Elemental K
Step 3: Calculate PPM Concentrations
A part per million (PPM) is simply one “something” per one million of “something else”. Where percent means “1 per 100”, PPM simply means “1 per 1,000,000”. PPM can be expressed either on a volume or weight basis. For nutrient solutions, PPM is expressed on a weight basis noting that 1 L of water weighs 1 kg. That is:
- 1 mg / kg = 0.001 g / 1000 g = 1 g / 1,000,000 g = 1 PPM
- 1 PPM of an element in water = 1 mg of the element / 1 kg of water = 1 mg/L
Converting elemental weight percents to elemental PPMs simply requires multiplying the total feed amount by the elemental weight percent. Noting that 1 mL of water (or solution) weighs approximately 1 g, the conversions are performed as follows for liquid and dry fertilizers:
- Liquid:
- 1 PPM = 1 mg/L = (ml Feed) * (Element wt% in Feed) * 10 / (L of Water)
- Dry:
- 1 PPM = 1 mg/L = (g of Feed) (Element wt% in Feed) * 10 / (L of Water) = (mg of Feed) * (Element wt% in Feed) * 0.01 / (L of Water)
The calculations above do not account for temperature effects on water density or for the increase in solution weight from the added feed, both of which are typically small enough to be neglected.
Step 4: Calculate Total PPMs
The PPM of each element in a final feed mix is simply the sum of each elemental PPM from each product divided by the total volume of the solution. For example:
- 2 L of Water
- 3 mL of Liquid Feed #1, 4-5-6 NPK
- 7 g of Dry Feed #2, 8-9-11 NPK
Results in:
- N – (3 x 4 x 10 + 7 x 8 x 10) / 2 = 340 ppm N
- P – (3 x 5 x 0.44 x 10 + 7 x 9 x 0.44 x 10) / 2 = 172 ppm P
- K – (3 x 6 x 0.83 x 10 + 7 x 11 x 0.83 x 10) / 2 = 394 ppm K
Notes
Label Values
Note that the guaranteed minimum values on the fertilizer labels are actually nominal minimum values. Products are allowed to be lower than the label values by a certain amount depending on each jurisdiction (e.g., see Cal. Code Regs. 3 § 2317.5). Products may also exceed the label amounts by any amount at any time. For example, companies may change product formulations and re-use existing labels and packaging as long as the minimum labelled amounts are still met and/or exceeded.
Individual ion measurements and/or laboratory testing is typically required to confirm actual weight percents for any specific product or formulation. However, typical label information is usually sufficiently accurate for most home cultivation purposes.
Other Units
Sources other than product labels (e.g., scientific articles, local water quality reports, etc) often use other units and nomenclature to report concentrations. Two of these include “Element As” notation and molar concentration.
The “Element As” notation is sometimes used to indicate that the listed value is actually an elemental weight percent (or concentration) while also specifying the molecular form of the element.
For example, “1% N-NO3-“ indicates a 1% concentration of nitrogen atoms in the form of nitrate molecules. In this case, the listed value can be used directly as an elemental value for the concentration of nitrogen atoms.
Scientific and technical literature will sometimes list concentrations in terms of molarity (M), which is the number of atoms (i.e., 6.02 x 10^23 = 1 mol) per liter of solution. One mole of atoms is equal to the atomic weight of the atom in grams. That is, moles/liter can be converted to g/liter by multiplying by the atomic (or molecular) weight. For example:
- 1 mM = 1 millimole/L
- 1 mM K+ = 1 x (39.10) = 39.10 mg/L Elemental K
- 1 mM N-NO3- = 1 x (14.01) = 14.01 mg/L Elemental N as Nitrate
- 1 mM BO(-3) = 1 x (10.81 + 3*16.00) = 58.81 mg/L Borate = 58.81 x (10.81) / (10.81+3*16.00) = 10.81 mg/L Elemental B
Relationship to Electrical Conductivity
Elemental ppm is not the same as TDS (Total Dissolved Solids) ppm, which is a measure of the total electrical conductivity of a solution converted to an equivalent concentration of Na (500-scale) or K (700-scale) ions that would give that same conductivity.
Growers typically use electrical conductivity as an indirect indication of the general overall strength (i.e., total elemental ppm concentration) of a solution. For this reason, it is best to clarify when one is specifically referring to elemental ppms (e.g., by using “elemental ppms”, “elemental concentrations”, “mass ppms”, “mg/L”, or similar).
The relationship between elemental concentration and electrical conductivity depends on the specific proportions and types of the individual ions in a solution, as well as the interactions between them. It is possible to add elemental mass without affecting the overall EC of a solution (e.g., when one species provides sufficient buffering capacity).
For a given ratio of elements, however, electrical conductivity is roughly linear with respect to concentration at the low levels typically found in nutrient feeds. As such, EC can be used as a rough tool for diluting a feed mix to achieve a certain strength (e.g., after accounting for the EC of the starting water). For example:
- Starting Water EC = 100 ppm
- Used to make concentrated nutrient feed with final EC = 1000 ppm
- Then, diluted with starting water to EC = (1000 - 100)*0.5 + 100 = 550 ppm
- Should have ~50% the elemental concentrations of the concentrated nutrient feed
This is mostly applicable to hydroponic and other systems that use concentrated feed mixes, injection systems, etc. to automate fertigation and irrigation. Based on the accuracy of the available measuring instruments (e.g., EC meter, gallon jugs, measuring spoons, pipettes, milligram scales, etc), measuring actual volumes and weights may be more precise than using electrical conductivity to obtain a specific elemental concentration for the home grower.
