##### Article by: Perry Romanowski

To become a college graduate with a degree in chemistry, you probably had to take at least a year of calculus and some type of statistical analysis. Then classes like Physical Chemistry or Inorganic Chemistry further demonstrated the complicated math that was required to be a scientist. Who remembers partial differential equations?

Well, if the math in your college chemistry classes wore you down, then we’ve got good news for you. Cosmetic chemists use almost no complicated math. In fact, all the math you need to know to be a cosmetic formulator, you likely learned in high school. Here are the top mathematical challenges faced by cosmetic chemists and how to do them.

### Cosmetic Chemist mathematical challenges

1. Figuring out % activity of an ingredient
This is one of the most common problems you’ll face. Most liquid raw material are not supplied as 100% ingredients but instead are water solutions (or other diluent). So, if you buy SLS it is usually sold as a 28% solution. You can find the activity of an ingredient by looking at the specification sheet. Usually, it is listed as % solids.

If you have a formula that calls for 30% SLS, the product doesn’t actually contain 30% SLS. It contains 30% of a 28% solution. By multiplying the % solids by the % required in the formula, you can find the % activity. Therefore, a formula calling for 30% SLS only contains 8.4% SLS. For formulators, this is the most important mathematical concept you must learn.

Math skill required – Multiplication

When creating formulas, you have to make sure everything adds up to 100%. Fortunately, this is fairly simple.

To make sure the formula adds up to 100%, you just need to add the percentages of all the ingredients in the formula. If they are higher or lower than 100, just add or subtract from the main diluent (usually water) to make it equal to 100. For example.

Water 78%
HEC 1%
Citric acid 1%
Cetyl Alcohol 5%
Cetrimonium Chloride 2%
Preservative 0.2%
Fragrance 1%

This conditioner formula adds up to 88.2%. You subtract that from 100 and you are left with 11.8%. This is the amount that should be added to your water % to make the formula square. So, the amount of water in this formula should be 89.8%

Math required – Addition and subtraction

3. Figuring out required ingredient amount
Frequently, you’ll inherit a formula and will have to figure out the amount of raw materials required to make a certain sized batch. This just requires simple multiplication.

First, determine the size batch you want to make. Next, find the % of the ingredient in the formula. Multiply the two numbers and your result is the required amount of the ingredient. For example.

Suppose you want to make a 500g batch of the conditioner in the example above. It calls for 2% of Cetrimonium Chloride. To figure out how much CC you’ll need, just multiply 500g * .02 = 10g. After you’ve figured out all the raw materials, add up the gram totals to ensure they equal the batch size.

Math required – Multiplication and addition

4. Figuring out HLB
When you’re formulating emulsions, HLB can help you figure out which emulsifier you need for your oil phase. Go see this previous post to see how to do cosmetic HLB calculations.

5. Converting units
It’s a fact of life in the US that industry continues to use Pounds and Gallons rather than Kilograms and Liters. In the lab, everything you do will likely be measured using the metric system. But when you take your formula to the compounding area, you’ll have to convert them to English units.

To convert your formulas, you just need to convert Kilograms to Pounds. This is done simply by multiplying the Kilogram mass by the conversion factor (1 kg = 2.2046 pounds). So, if your formula calls for 25 kg of Cetyl Alcohol, you’ll need to add 51.15 pounds of it.

For liquid measurements, it’s usually necessary to figure out how many gallons of an ingredient you need. If the specific gravity of the liquid is 1 (as it is for water) then you simply take the Kilograms required and divide by the conversion factor (8.35 Kg per gallon). So, 44 kilograms of water is really 5.27 gallons.

Perhaps the easiest way to do these conversions is to look them up on Google or use a conversion calculator like this one.

### The Mathematical Cosmetic Chemist

Once you have systems set up to do these calculations for you (like automated spreadsheets), there is even less math required to be a cosmetic chemist. But math is good for your brain so even if you have a computer that calculates these things for you, you should practice them to ensure you know how to do them.

The last thing to mention is statistics. There is some statistical math that you’ll have to do on occasion but it’s more complicated than this post can allow so we’ll write a separate entry on the statistics of cosmetic science.

1. Kel

2. Kel

Is a chemist able to determine the percentage of chemicals used in a product (for example, a hair product) by analyzing it? I’m interested in how close “generic” products which claim to be dupes of another product actually are.

1. Perry

While a chemist is not able to exactly analyze the % of chemicals in a formula, we can get pretty close. It really depends on the product but there really aren’t any personal care formulas that can’t be suitably duplicated.

3. Kelly

Hi Melina,
In the US, UC (OH) and Faleigh Dickinson (NJ) are the only programs I know of with cosmetic chemistry focus. The UC masters program is available on-line so it does not require you to move, but you have to visit campus for a two-day laborotory course. Because in my opionion, solely listening to lectures is no substitute for the hands on experience these programs provide.

4. melina vega

Is UC the only college that has classes of cosmetic chemistry? Because I don’t think I’m willing to move.

Thank you Kelly.

6. Kelly

It really depends on the type and strength of claim you are trying to make. If you want to clearly link the extract to an efficacy claim you want to have supporting data. Often times suppliers use in vitro test methods to make recommendations for use level, but ideally you want significant in vivo data to validate your claim. Claims also have legal and regulatory implications so it is best to err on the side of caution. Hope this helps. -Kelly

1. Aye

Please let me know how to calculate 5 to gram.

Thank you for your answers Kelly and Perry. Another question that arises is how to know the concentration of active substances in the extract that we may use in its formula to ensure efficacy without having to get into a clinical study.
Is it enough to trust the supplier’s recommendations or doese exist any other information sources where a cosmetologist can find happiness.
Thank you and excuse the newbie questions 🙂

8. Kelly

I would also suggest single sourcing extracts if the specifications and extraction methods do not match exactly between suppliers because chemical composition, solvents, and preservatives often vary considerably. So even at low concentrations in the final formulations the differences may manifest in efficacy as well as instability of color, odor, preservative efficacy, etc.

Thank you for this information. I have a “math” question concerning the use of extracts. In some formulas we used a certain percentage of a certain extract but when you do a search we find that suppliers present it in different concentrations (which depend on the extraction method) and even sometimes in the form of dry extract. I would like to know how to solve this mathematical problem in choosing the exact percentage in his formula.

1. Perry

Typically when you make a formulation you limit the number of suppliers for any ingredient to 2 or 3. Then you set a specification for those suppliers that they have to provide you material at a certain active %.

But if you are going to use different % concentrations then you’ll want to figure out the % active in your formula.

10. sal

Thanks for this great info. I am starting my own hair product company and was trying to figure the 100% of my formulae for the manufacturers this really helped.

11. Perry

Typically, a scientific paper will report the %active, so in your example, 10% azeloyl glycine is = 10% active azeloyl glycine. If the product is supplied as a 30% solution, this would mean that 33% of the formula would be azeloyl glycine.

12. Viv

Hi Perry,

When it is reported in scientific publications that X percentage of an active ingredient was considered effective for ‘whatever’ effect, how does that correlate to the percentage used in the formulation; e.g. if a paper relates that 10% azeloyl glycine is effective for reducing pigmentation and Azeloyl glycine is sold as a 30% solution; what is the percentage used in the formulae? When looking at example formulations given by the producers of the active ingredients, does the % relate to the activity of the ingredient?

13. Chemstu

Yes please! I would like him to write a post too! Also sometimes in color we make concentrated pigments (usually around 10-12%) but we have to convert it back to the dry amount for the scale up in the plants. Nothing major again.

14. Kelly Dobos

Agreed, statisics and their proper application to data are way too heavy for one blog post. But essential to good decision making and for substantiation of product claims. I highly reccomend the two stats courses in the UC Cosmetic Science program which can be taken online. The classes are extremely thorough and in depth, but well worth the effort if you have the motivation!

1. Perry

I was going to see if the resident Chemists Corner statistics genius would be willing to write a post about the type of stats used by cosmetic chemists.

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