# Blog Archives

## Ingredient Math – estimating worst (or best) case for ingredient proportions

Have you ever wondered how much of a certain ingredient is really present in a sweet, or any food product?

You probably know that ingredients are listed on food labels in order or prevalence, with the most predominant ingredient first. You may have even known this was determined by weight. But in this article I will discuss a method to get an estimate for the maximum of each ingredient’s percentage of total weight – just by using the ordered ingredient list.

To derive this formula, lets start with a very simple example, a product with just “coffee and sugar”. Since coffee is listed first we know it has higher or equal amount of total weight when compared to sugar.

Is there anything we can do to determine about how much the first ingredient, coffee, is really in the product? The answer is no because coffee could be almost 100% to almost 0% of the total weight, with sugar filling in the remaining space. (Actually, there is a trick to determine the amount here since the second ingredient is sugar, which I’ll discuss later in this article).

But what about the sugar?

Well, if you think about it, there can’t be more than 50% sugar, by weight, since any more of that would mean there was more sugar than coffee, which we know is not the case.

So we’ve learned something important – that there is no more than 50% sugar in the product. This would apply to another second ingredient when there are two total ingredients.

What if there were three or more total ingredients? We would get the same result, because the other ingredients could be in trace amounts (practically 0%), so the “50% maximum for the second ingredient” rule would still apply.

What about the maximum amount of the third ingredient? Using the same logic you will see it cannot be above 33.3%, since any more of that would mean it is in greater proportion than the first and second ingredients. And for the forth ingredient you get a maximum, by weight, of 25%.

Turning this into a simple formula we get the following:

Maximum percentage of the Nth ingredient = (100 / N)

So for the 5th ingredient, you would get (100 / 5) = 20% maximum weight of that ingredient.

If you use formula along with the serving size you can determine the maximum weight of any of the ingredients per serving. Pretty handy if you want to minimize your intake of certain things.

If you want to take this to the next step, you can infer more information when one more more ingredients are a type of sugar. For example, if a product contains “coffee, sugar” and has 3 grams of sugar per 15 gram serving, then you know right away there is 20% sugar and 80% coffee in this product. Keep in mind that the grams of sugar listed includes any type of sugar, so if you have multiple ingredients which contain some type of sugar (even fruits) then the calculation gets a little trickier.

Besides knowing there is a certain percentage of sugar, you can use that to deduce information about other ingredients.

For example, if the imaginary product I just described had a third ingredient, say “coffee, sugar, vanilla”, then you would know that there is 20% or less vanilla because sugar is 20% or less. This assumes that there is no sugar in the vanilla, otherwise it would be harder to make any definitive conclusions.

Similarly, if you know how much protein is in each ingredient, you can figure out even more using the supplied protein in grams.

You can also leverage information about other ingredients to deduce additional information about the other ingredients. For example if a product had “milk, sugar, guar gum, vanilla”, you would know that the proportion of vanilla is much less than 25% since guar gum is typically used in relatively small doses. (I’ve tried overusing guar gum in homemade ice cream – its not pretty!)

I love thinking about food and ingredients from a methodical, logical point of view since it allows me to apply science to my everyday life.

**References**