# Math Used in Cosmetic Product Formulation

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

2. Adding up formulas
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.