The Math and Science Bit

A handy hydrometer illustration

I promised a long time ago, in my very first post, that I'd explain the math involved in using a hydrometer to measure and predict the alcohol content and dryness of your mead or other homebrew (mostly mead, as I'm not really qualified to talk about anything else just yet).  I promised that so long ago, but that was before I was laid off at my old job and things have been understandably crazy since then, but now I'm inspired to finally bring you this information.

Mostly this is for my mead mentor Amber, who is incidentally at her blog talking about mead she is working on and other things.  She mentioned how I never properly explained this math to her, but it is useful to anyone who spent the six bucks for a hydrometer!

To start with, reading the hydrometer and what it actually means.  The hydrometer is a weighted glass tube that floats vertically in a water solution and reveals the specific gravity of the solution.  The specific gravity is based on the sugar content of the solution and is measured numerically from 0.990 and up (but we won't really need too large a range as small changes make a big difference).

During fermentation, the yeast convert the sugar into alcohol and the specific gravity goes back down.  For reference, a change in specific gravity of 0.0075 creates approximately 1% alcohol by volume.  So we can look at the before and after fermentation measurements of specific gravity and calculate the alcohol content.  Warning! Math ahead:

You should have a couple of measurements at this point:

• Initial Specific Gravity (i);
• Final Specific Gravity (f);

Which we will take and find:

• Change in Specific Gravity (ΔG)
• Equal to (i-f);

Which will give us:

• Percent Alcohol by Volume (P)
• With (P=133*ΔG).

Now, the 133 is a number that has a lot to do with differential equations across volume, chemistry and physics, and some extra science you don't need to know.  Just take it for granted that someone else has done this really complicated part to make this math as easy as possible for you.

Also, since the measurement after fermentation is a literal measurement of how much sugar is left in the solution, it can tell us how dry of a drink we've made.  The scale for measuring dryness isn't exact, but there are some approximate guidelines that are generally agreed upon:

• Dry 
• 0.990 to 1.006;
• Medium
• 1.006 to 1.014;
• Sweet
• 1.014 to 1.020;
• Dessert
• 1.020 and up.

Now, this final reading and this scale can tell us what we ended up with or it can allow us to predict what we would like to make by setting our goals for (P) and (f) and determining the (i) for which we need to aim to achieve the desired results.

For reaching such a specific target, we need to set up our goals. Though maybe not the easiest decision when considering the ingredients and flavors involved in your recipe, it's a little simpler to decide how dry you want your final product.  Once you have a desired dryness, just pick a target (f) within your range.

Slightly more complicated is deciding on the desired alcohol content.  First, you should know a little something about your yeast, especially it's alcohol tolerance.  Every yeast has an alcohol content that is too high for it to survive and a natural cap to how much it can ferment.  If your local homebrew store can't give you this information, it is readily available for most major brands on yeast reference tables like this one.  You can't plan for a (P) higher than your yeast can tolerate.  On the other side, if you want to ensure something very sweet, you can use a yeast that you know will stop and not over-ferment and leave you with something that's too dry.  Otherwise, once fermentation slows down you can take regular readings until you have reached the desired dryness and then stopping fermentation manually.

In any case, once you decide on your desired alcohol content, you just use the reverse engineered formula:

• Desired Alcohol Content (P);
• Desired Final Specific Gravity (f);
• Gives Target Initial Specific Gravity (T)
• T=(P/133)+f.

As you mix up your solution before fermentation, you can add more honey or any other ingredient you have with more sugar to raise the initial specific gravity, or conversely water or any ingredient with less sugar in it to lower the initial.  Once your hydrometer says you've hit your goal, you have a very predictable and controllable fermentation cycle ahead of you!