Making Limoncello, Part 2: The Math

So we’ve got our lemon zest infusion going and it’s going to do its thing for the next month or so. That gives us time to prepare for the next steps. Specifically, that means figuring out how to make a simple syrup to mix with the infused spirits to give us a finished product that has the target alcohol and sweetness we want.

Alcohol By Volume (%ABV)

ABV is the measure of how much ethanol is in a liquid. We can reduce the %ABV of a spirit by simply diluting it with another liquid. For our limoncello, that liquid is going to be a simple syrup made from granulated sugar (sucrose) and water, but more about that later.

Suppose we start with 100mL of 100 proof alcohol (that’s 50% ABV) and add 100mL of water or simple syrup—or anything, I suppose, that doesn’t add more alcohol. We know intuitively that the resulting mixture will be have the same amount of alcohol but twice the volume, or 25% ABV. We can think of this in more concrete terms this way: Of the original volume (100mL), 50% (50mL) was pure alcohol. Once we add the water, we still have the same 50mL of alcohol but now it’s contained in a mixture that totals 200mL in volume. 50mL ÷ 200mL = 0.25, or 25% alcohol.

Target ABV

If we start with an infusion of 151 proof (75.5% ABV) Everclear, we will need add some volume of a simple syrup to achieve our target ABV. Before we can do that, we need to answer some important questions.

First, what do we want the target ABV to be? Suppose we want our finished limoncello to have 30% ABV, or 60 proof. Let’s also suppose that our infusion has 1.75L of 151 (75.5% ABV). We know the amount of alcohol in the original spirit is 1750mL × 0.755 = 1321mL. To get a final solution that is 30% ABV, we need to add some amount of liquid so that the 1321mL of alcohol is only 30% of the total volume. Mathematically,

To figure out how much liquid to add, we simply solve for x, which in this case is 2654mL.

Simple Syrup

So we need 2654mL of simple syrup. Simple, right? Not so fast.

There are two more important questions we need to answer. How sweet do we want the final mixture to be, and what does the sugar-to-water ratio need to be?

Let’s start with the sweetness, which we express in grams per liter. How sweet is sweet? The table below lists the sugar content of some common liqueurs, according to Diffords Guide.

For our purposes, let’s target a sweetness of around 200g/mL. Now let’s figure out how much sugar we need. For a target volume of 4404mL (the original 1750mL + the 2654mL of syrup) there needs to be 881 grams of sugar in the syrup. Here’s the math:

Cool, now how much water? We need to make solution of sugar in water with a total volume of 2654mL, but we can’t just use 2654mL of water because the sugar contributes something to the volume too. But how much? For that we need to know the mass density of table sugar (aka sucrose), which happens to be 1.59g/mL. In other words, for every 1.59 grams of sugar we add to water the volume increases by 1mL. Using that information, we can compute the volume that 881 grams of sugar will contribute to the syrup, as follows:

Of the total volume (2654mL) of simple syrup, 554mL will come from the added sugar. The rest (2654mL – 554mL = 2100mL) is water. So we’ll prepare the simple syrup by adding 881g of granulated sugar to 2.1L of water.

Now that we know how to prepare the simple syrup to achieve a desired %ABV and sweetness, we’re ready to make the syrup, mix it with the infused alcohol base, and bottle, all of which I’ll share in a future post.