Math for cosmetic FormulatorsPractical Cosmetic Formulating

Perry Romanowski

Hi and welcome to the basic math for formulators module.

One of the things that surprised me when I first got started in the cosmetic industry was that there really wasn’t any complicated math required to do my job as a formulator. I thought of all those difficult Calculus courses I took and the crazy partial derivative calculations I had to do in Physical Chemistry and I was amazed that none of that applied to my job.

The math geek in me was disappointed but if math is something that wore you down, then I’ve got good news for you. Cosmetic formulating uses almost no complicated math. In fact, all the math you need to know to be a cosmetic formulator, you likely learned in high school or even earlier. ——As always, let’s start with the objective of this lesson. I’ve created this lesson to remind you of all the basic math skills you need to formulate cosmetics and complete this course. Don’t worry, it really isn’t that difficult.——Alright, let’s look at where and when formulators use math.

You are going to have to use math whenever you are

Creating formulasCalculating the amounts of raw materialsConverting measurementsCreating ingredient labelsCalculating formula costs

There are other times when math is used but we will go through those procedures in some later course modules. The 5 techniques listed here are required background information.——The nice thing about formulating math is that all the skills you need to do it were things you should have learned in grade school or high school.—The primary skills you’ll need to be comfortable with include

Addition and SubtractionMultiplication and division

Multiplication and division come in to play when we calculate things like percentages, fractions and conversion measurements.

The nice thing about this lesson is that unlike school you can use a calculator or computer whenever you want. During the course I will also present you with spreadsheets you can use for formulating that

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already have the math formulas added. You simply have to type in the numbers.

——Alright, let’s move on to the math used in Cosmetic Formulas.

One of the primary differences between cosmetic formulas and cooking recipes is that the formulas are based on the mass (or weight) of ingredients rather than the volume. Food recipes typically are given with measurements like cups, tablespoons and teaspoons.

This isn’t how cosmetic formulas are done. Instead, cosmetic formulas are written in terms of percentages. This is done because it gives you the maximum level of flexibility. It is very simple to change the size of your batches when the formula is written in percentages. It’s also much easier to change the level of ingredients to see what effect if might have on the final formula. This will be of crucial importance when you are creating different prototypes.

——Here is an example formula. We’ll talk about the characteristics of a formula later but for now I want you to focus on the column where it lists the % of the ingredient in the formula. This is where the math takes place.

——So when you are doing calculations for a formula you have to remember that the total amount of the formula percentage always has to add up to 100 percent. That means in the formula I showed you that percentage column must add up to 100.

To calculate the amount of any raw material you need for a given batch size, you simply need to multiply the Mass of the batch by the percent of the ingredient in the formula.

Let me go through an example to make it more clear.

——Here is a simple hair conditioner formula. This formula has about 5 ingredients but at the moment it is just water which is equal to 100 percent.

——Now, suppose we add in our cellulose thickener at 0.5% of the formula. The total number has to continue to add up to 100% therefore we need to remove some of the percentage from an ingredient. And in this case (as is the case for most formulas) we remove it from water. So now water is equal to 99.5% of the total and cellulose is 0.5% of the total. They still add up to 100% though.

——Next we add 1% of cetrimonium chloride. Again the total of all the ingredients has to equal 100% so we subtract 1% from the water and it now makes up 98.5% of the total. ——In this formula we have 2.5% cetyl alcohol so we’ll have to remove that much from the water bringing it’s total down to 96%. Notice that all of these numbers added together continue to equal 100%.

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——Finally, we finish the formula with fragrance, preservative, etc. This makes up 1% of the formula so we need to remove that much from the water leaving 95% in the formula.

So there you have it. To properly calculate a cosmetic formula the percentages of all the constituent ingredients must equal 100%.

——Now, let’s look at how you calculate how much of an ingredient you put in a batch. Remember the formula I showed you? We focused on the percentage of the ingredients in the formula. Now, I want to show you how to calculate the amount of each ingredient in a batch. The key pieces of information you need is the batch size and the percent of the ingredient in the formula.

——Calculating the amount of the ingredient that you need to use depends on the size of the batch you are making. You can calculate it by following these simple steps.

1. Determine the size of the batch you want to make2. Multiply the ingredient percentage by the total amount (ignore the % sign) 3. Divide that answer by 1004. That’s how much you use

Alright, now let’s go through an example.

——Suppose you had the simple conditioner formula we just described and you wanted to make a 200g batch. How would you figure out the amount of each ingredient that you needed?

——Simply follow the steps I described. Multiply 200 by the percentage and divide by 100. So in the case of water, you multiply 200 by 95, then divide by 100 which totals 190. Similarly, the amount of cellulose you need is 200 times 0.5 divided by 100 which is 1g.

Notice that the sum of all of the masses should equal 200g. If it does not equal your starting total something is wrong.

——Let’s look at what a 600 g batch would look like. You calculate amounts the same way but instead of multiplying by 200, you multiply by 600. So the amount of water is equal to 600 times 95 divided by 100 which equals 570.

If you want to verify the amounts feel free.

——Here is an exercise I want you to try yourself. Feel free to use a calculator. You can pause the lesson

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now and calculate the numbers or you can do it after you finish this lesson. I’ll also provide the answers so you can check your work. You should get good at this because this type of math is something you will be doing frequently.

——Alright, let’s move on to our next math topic that formulators have to do. Conversions.

While most professional cosmetic labs use masses and percentages for their formulations there are some older formulas you might run into or some kitchen, DIY formulas that are written in terms of volume. Also, when your formulas are scaled up, the manufacturing people frequently want you to convert the liquid produce to volume rather than mass.

Some of the primary conversions you’ll run into as a cosmetic formulator include

Converting Fahrenheit to CelsiusOunces to gramsGallons to liters

——There are lots of useful online tools like the one mentioned here but it’s incredibly helpful to memorize some of the key conversions. For example, the conversion factor for ounces to grams is 28.35. This is really helpful to remember. Also, the number 3.79 which converts gallons to liters is helpful.

——If you are more used to the kitchen than a chemistry lab, you will find these approximations useful. These are approximations because these are conversions from a volume to a mass and the true value actually depends on the density of the ingredient. However, for our purposes these approximations are close enough for most cosmetic ingredients.

So, 1 teaspoon is about 5 mL which is equal to about 5g. 1 tablespoon is 15 mL or 15 grams. A quarter cup is 59 mL while a cup is 236 mL. Again all of these mL values are approximately equivalent to grams to make the calculations easier.

——Here are some examples.

To calculate how many grams you need when the formulas calls for 8 ounces, simply multiply 8 by 28.35 (our ounces to grams conversion factor). So, 8 times 28.35 is 226.8 g.

Similarly, 3 ounces is multiplied by 28.35 to get 85.1g.

When you are converting gallons to liters the multiplication factor is 3.79. So 2 gallons of water is equal to 2 time 3.79 or 7.58 liters.

Finally, you will frequently see temperatures in both Celsius and Fahrenheit. To convert from Celsius to Fahrenheit you multiply C by 9/5 and add 32. So, 4C is equal to 4 times 9/5 plus 32 or 39.2 F.

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I encourage you to do the practice conversions I’ve listed in the exercises pages related to this lesson.——Alright, on to our next place where math is used. Ingredient Lists.

On cosmetic products around the world you are required to list ingredients. And in most places you have to list them in a specific way. cosmetic chemists are typically the ones responsible for determining the order of those ingredients.

——Here are the rules that most places follow. Ingredients must be listed by concentration if the ingredient is in the formula at a concentration higher than 1%.

The concentration of an ingredient is based on it’s percent activity.

That just means the amount of non-solvent material in the sample. Sometimes this number is also referred to as the percent solids.

——So, you will need to figure out what we call the “activity” of an ingredient. Since many raw materials are sold diluted with some kind of solvent you need to calculate how much of the actual ingredient is in there. For aqueous ingredients you can figure out the % solids by subtracting water from the total to mass of the raw material.

For example, Ammounium Lauryl Sulfate (or ALS) is often sold as a 28% solution in water. What that means is that 72% of the sample is water and 28% is ALS.

Similarly, natural extracts are typically solids as 1% active solutions in water or propylene glycol. That means that 99% of the sample is solvent and 1% is actually the extracted material.

——Now, let’s look at how you might calculate how much of an ingredient is in your formula.

You can do this in a simple three-step process.

Step 1 - Find the percent of your ingredient in the formulaStep 2 - Multiply that number by the % activity of the ingredientStep 3 - Divide that number by 100

This will result in the actual amount of the ingredient in your formula.

——So let’s return to our formula example. Take a look at ingredients number 4, 5, 6 and 8. You can see all of these ingredients have a % listed in their description. This just means that those raw materials are not 100% active. Which as we’ve seen they are made up of more than just the ingredient. In all of these cases, the additional material is water.

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——When calculating the amount of an ingredient in the formula you just follow the three step process.

In the formula posted, there is 32.143% ALS listed in the the formula. But we also know that the ALS is only 28% active. Therefore, we can calculate the total amount of ALS that is actually in the formulate by multiplying 32.143 by 28 and then dividing by 100. So, 32.143 times 28 is equal to 9.00 or 9 percent.

——Now try some exercises.

How much actual SLES is in the formula.

Remember 4% was listed as the amount in the formula and it is a 25% active ingredient.

Think about how you would calculate that answer.

Now try to figure out how much actual Cocamidopropyl Betaine is in the formula.

It was listed in the formula as 7.143% and you were told it is a 35% active ingredient.

Learning how to calculate these percent actives is crucial for understanding both how much of the ingredient is actually in the formula and for putting together your ingredient list. We will go through ingredient lists in a future module but knowing this background math will make it much easier.———

The final math topic we will cover is calculating formula costs. As a formulator you will have to know how much your formula costs to produce. Not only will this give you a good idea of how much of an ingredient you can use, it will also give you a good idea of whether the formula is viable. There is a formula cost that is just too high for most markets.

To calculate the cost of a formula you will need the formula and the cost of the raw material. Then it is just a simple four-step process.

Step 1 - Start with the raw material costStep 2 - Get the % of the ingredient in the formulaStep 3 - Multiply the cost by ingredient %Step 4 - Divide by 100

Let’s look at an example.——Here is an example formula with a list of the ingredient percents and the cost of the ingredients in terms of cost per pound. Since we started with cost per pound, our answer is going to be in cost per pound of the formula. If you work in Euros and Kilograms you can use this same procedure. Your answer will just be in euros per kilogram.

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So you can see that this formula costs a total of $0.44 per pound. To calculate each of the component ingredients you just follow the 4 step process. For example, the Fragrance in this formula costs $20 dollars per pound. It is in the formula at 0.5% so multiply 20 by 0.5 and divide by 100 to get $0.10. Therefore, the fragrance in this formula makes up 10 cents per pound. Similarly you can see that ALS makes up 18.8 cents per pound. The number is figured out by multiplying 25 by 0.75 and dividing by 100. ——Here is an exercise for you. See if you can figure out the total cost of the formula and the cost of each constituent ingredient.

———So there you have it, nearly all the math you need to use in formulating cosmetics. In review we covered the math needed for

Creating formulasCalculating raw material amountsMeasurement conversionsCreating ingredient labels and calculating costs

I hope you’ll agree that it wasn’t too difficult. However, even if you found these examples challenging in this course we provide some automatic solutions to a lot of these math problems.——

The thing to remember is that if you can do this simple math, you won’t have any problems with the math in this course.

Thanks for watching and I’ll see you in the next video.

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