Beer Math – Mix, Mix, Mix!

I’m going to take a break this month from previous months’ articles on the basic calculations and how they relate to the example American IPA recipe, and talk about the formula for mixing worts, musts, beers, meads, etc. – a topic that’s actually come up a few times in my life recently.

Recently, I was making a mead and wanted to add fruit juice to the must but needed to know how much honey to add to reach my target OG before adding the juice. The following formula will get you that answer, along with many other mixing questions that we’ll explore below:

Aa + Bb = Cc

It’s a pretty simple formula, but let’s break it down.
A and B – different quantities of liquids being mixed (volume of beer, mead, juice, etc.)
a and b – the conditions of A and B above (specific gravity, ABV, temperature, etc.)
C – the sum of the quantities of A and B (so, C=A+B)
c – the resulting condition of C
One note on this, all units of need to be the same for A, B,C, and a, b,c – no mixing here!

With that information, lets’ look at a few examples of how this would work for the homebrewer.

Example 1 – Mixing Two Worts
If I wanted to mix two worts – a 10L batch of 1.060 and a 12L batch of 1.045 – what would the final OG be of this new 22L batch? From this information, we can get everything except c, so let’s figure that out.

Aa + Bb = Cc
(10 L * 1.060 SG) + (12 L * 1.045 SG) = (10 L + 12 L) * c
10.6 SG + 12.54 SG = 22 * c
23.14 SG / 22 = c
c = 1.052

So, when we mix those two worts together, we’ll get a specific gravity of 1.052.

Example 2 – Fortifying A Wine

How much 35% brandy would I need to add to my 20L batch of 12% wine to get a final ABV of 19%?

Aa + Bb = Cc
(20 L * 12%) + (B * 35%) = C * 19%

This one looks a little more complicated as we’re missing two values, but we know that C = A + B

(20 L * 12%) + (B * 35%) = (20 L + B) * 19%
240 + 35B = 380 + 19B
380 – 240 = 35B – 19B
140 = 16B
B = 8.75L

So, if we want to fortify our 20L batch of 12% wine to 19%, we’ll need 8.75L of 35% brandy, and will end up with a final volume of 28.75L.

Example 3 – Combining Finished Mead With Fruit Juice

For this example, let’s assume you’ve made a 19L batch of 14% mead, and want to add 2L of tart cherry juice post stabilization – what would you final ABV be?

Aa + Bb = Cc
(19L * 14%) + (2L * 0%) = (19L + 2L) * c
266 + 0 = 21 * c
c = 266/21 = 12.67%

So, after adding that 2L of juice, our batch is now 21L at 12.67%

The above example can also be written a different way when b is zero as follows:

C1*V1 = C2*V2

This is a simple volume (V1 and V2) and concentration (C1 and C2) formula, that shows up a lot.

Before I end this month, I’ll go back to my original problem I had when I was making a batch of mead. I wanted to make and 11.5L batch of 1.050 mead with 1L of 1.030 cranberry juice, so what gravity did I need to make the must before adding the juice?

Aa + Bb = Cc (in this example, I use A for the must, and B for the fruit juice)
(10.5L * a) + (1L * 1.030) = (10.5L + 1L) * 1.050
10.5a + 1.030 = 12.075
10.5a = 11.045
a = 1.052

So, to make this batch of mead, I made 10.5L of must at 1.052 SG, then added 1L of 1.030 cranberry juice that gave me my final 11.5L batch at 1.050 SG.

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