# What PAC Is, and How to Calculate It

A closer look into one of the most ubiquitous acronyms in the Gelato-making world.

If you are a nerd like me and have been doing your gelato-making homework, you will have often come across the acronyms PAC, AFP and/or FPDF. They stand for ‘Potere Anti-Congelante’ (the Italian for ‘Anti-Freezing Power’) and ‘Freezing Point Depression Factor’, respectively.

What all these acronyms refer to is the lowering (or depression) of the freezing point of water that certain ingredients in the recipe cause. By comparing the freezing point depression of each ingredient in proportion to their quantities, we get a number from which we can derive how much lower the freezing temperature of the water in the recipe will be.

This number is called PAC (or AFP, or FPDF) and is used extensively in the ice cream and Gelato industries as an indicator of scoopability and serving temperature. Essentially, the higher the PAC, the softer the cream and the lower the serving temperature. Makes sense, right? If I make water freeze at a lower temperature, it will be softer at my current temperature.

So how does PAC work? And how can I calculate it for my recipe?

Let's have a closer look.

[Note: throughout this article I will use PAC to refer to all above, for simplicity].

"1 PAC unit corresponds to the freezing point depression power of 1gr of sucrose dissolved in 100gr of water (i.e. a 1% solution)."

As I mentioned in this article, sugars (but also polyols and salts) have the capacity of lowering the freezing point of water. To understand the mechanics of how this happens, we have to talk a bit about Solutions. In chemistry, a solution is a special type of homogeneous mixture composed of two or more substances. In such a mixture, a solute is a substance dissolved in another substance, known as a solvent. What is key about solutions is that the solvent and the solute bind together and a sort of chemical mating happens.

Water + sugar (in which water is the solvent and sugar the solute) are a classic example. So is water + salt, and water + alcohol.

Not all substances will dissolve in water though. Water + oil (or any fat for that matter) won't bind together, so you will end up with a different type of mixture, which we will discuss in a future article.

In the case of water-based solutions however, an interesting thing happens. , Take the case of water + sugar for example. Not only the sugar will make it taste sweet, it will also lower (depress) the freezing point of water. The same happens with water + salt, and with water + alcohol.

This has many useful applications (think spreading roads with salt in winter to avoid ice forming), but for Gelato and ice cream making it is crucial, because it is by lowering the freezing point of water that we manage to get creamy delicacies at sub-zero temperatures (remember, water freezes at 0ºC at sea level).

But to what extent will sucrose lower the freezing point of water, you may ask? That is a very good questions, but one that we will leave for a future article. Because it is not important for our PAC calculations, You see, PAC is just an index, a relational figure, which tells us the potential that our ingredients have to lower the freezing point of water. So all we need to focus on now is to define what is the reference of this index.

As we already discussed in this article, there are many types of sugars. Sucrose being the most common and by far the most used in Gelato (and ice cream) making, it is only natural that it has been chosen as reference.

With that in mind, some very clever people established our unit of reference as that which corresponds to the freezing point depression power of 1gr of sucrose dissolved in 100gr of water (i.e. a 1% solution). In a massively creative stunt, they called this unit Sucrose Equivalent (SE); which incidentally is just a more scientific acronym, but is essentially the same as PAC, AFP, or FPDF.

So if you take a glass with 100gr of water, add 1gr of sucrose to it you will end up with a PAC (or AFP, or FPDF, or SE) of 1. Add another 4gr of the sweet stuff and you will end up with a PAC of 5.

Simple, huh?!

So now that you know what it is, shall we get to grips with how to calculate it in a recipe?

If we only had sucrose and water in our recipes it would be easy, just calculate how many grams of sucrose the recipe has in proportion to 100gr of water. Since most recipe dosages are determined per kg, all you have to do is divide 100/1000 (remembering that 1lt of water = 1kg) and you will find the total PAC of your recipe. As simple as that!

Of course, a Gelato made only with water and sucrose would probably taste rather dull. So we have to find a way to convert other ingredients to PAC so that we can know the total PAC in a recipe with several different ingredients (and get a bit more flavour out of it).

As we mentioned earlier, this can all be calculated if we know the molar mass of our ingredients. But you probably want to spend your time in the lab or kitchen making delicious Gelato instead of tinkering with an Excel spreadsheet and a chemistry encyclopaedia, so I put together a nifty table that lists the PAC of several common ingredients:

You then calculate the amount of any of these substances that appear in our recipe, always in proportion to 100gr in 1,000gr of water. One thing to keep in mind is that some of these ingredients are not pure sugars / salts / polyols. So it is key to apply the values on the table only to the sugar / salt / polyol component of the ingredient.

Sounds complicated? It is not. Let's do a few examples and you will get the hang of it in a snap.

For that, let's use the following recipe for a very simple fior di latte:

The first step is to find all ingredients containing substances that will have an impact on the water's freezing point and isolate their quantities [we will call these substances components]. There are many more, but for practical purposes we will focus on the four main groups that can have a meaningful impact on the overall PAC of a gelato recipe: sugars, polyols, alcohols, and salts.

So in the recipe above we will have the following:

• Milk: 4.9% lactose
• Cream: 2.8% lactose
• Sucrose: 100% sucrose
• Dextrose: 92% glucose

Applying the figures above to the recipe and crossing with the PAC equivalence table, we get the following:

So we can say that the recipe above has the equivalent freezing point depression power of a solution with 24.2gr of sugar in 100gr of water.

And ecco qua!!, this is how the PAC of any recipe can be calculated.

Most Gelato balancing software will perform these calculations automatically for you, but now you know how they do (or should do) it. And if you don't have a Gelato balancing software yet — or don't plan to get one any time soon — worry not, I prepared this nifty spreadsheet so that you can always come back, enter the ingredients of your recipe and their parameters in the yellow boxes, and it will calculate the overall PAC for you.

[please note that clicking on the image will open the spreadsheet in a new google sheets window]

Nifty, huh?! :)

"If you compare two recipes, everything else being the same, the one with the higher PAC will be softer at the same temperature in the cabinet."

That whole calculation is all very nifty and clever, but why do I need to know this, you might be asking?

The answer to that question is twofold:

First and foremost, knowing the PAC of your recipe will give you an indication of its potential to lower the freezing point of water. And since water is soft and ice is hard, the lower the freezing point, the softer your cream will be. So although there are a few other key factors at play (which I will discuss in a future article), by knowing the PAC of your recipe you will have a rough indication of its hardness potential. What this means is that if you compare two recipes, everything else being the same, the one with the higher PAC will be softer at the same temperature in the cabinet.

Second, by trial and error, Gelatiere have developed a few rules of thumb for knowing how a typical Gelato recipe will behave in the cabinet. So by balancing your recipe to standard values, you will be able to have a cream behaving to industry standards. This rule of thumb applies as follows:

For milk Gelato: PAC ÷ 2 = ideal serving temperature for scoopability. Recommended PAC range is between 24–28 for a serving temperature of -12º to -14ºC.

For Sorbettos: PAC ÷ 2.5 = ideal serving temperature for scoopability. Recommended PAC range is between 30 and 36 for a serving temperature of -12º to -14ºC.

* All the above are references only and can vary from artisan to artisan according to personal preference.

Now, there are severe limitations to this trick — not least because scoopability is influenced by a few key factors other than PAC — but for practical purposes it is a good reference if we take it for what it is: a starting point.

And being of widespread use in the industry, it is a good thing that anyone intending to balance their own recipes knows how it works.

In a future article I will discuss a more objective method to calculate scoopability and serving temperature which includes two other key factors. But for now you should have a good grip of what PAC is, how to calculate it and what is its use.

Bravo!!

1. PAC stands for 'Potere AntiCongelante' and is the same as AFP (Anti Freezing Power); FPDF (Freezing Point Depression Factor); and SE (Sucrose Equivalent).
2. It indicates the potential a substance has to lower the freezing temperature of water compared to that of 1gr of sucrose diluted in 100gr of water.
3. You can calculate the PAC of a substance by using its molar mass, or use handy tables that provide a number for several different ingredients.
4. Conversely, you can calculate the overall PAC of a recipe by factoring the PAC of individual ingredients and their dosages. Example: milk has 4.9% lactose, which has a PAC of 100. So 500gr of milk will have a PAC of 2.45, while 1,000gr of milk will have a PAC of 4.9.
5. The total PAC of a recipe will influence its hardness in the cabinet, so it is important to keep it within recommended ranges when balancing.

A presto!!

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