# How is ABV calculated if distilled spirits are added to beer?

How would one calculate the ABV of a beer if distilled spirits were added? For instance, when making a beer recipe that called for adding bourbon as a flavoring agent. If you started with, say, 5 US gallons of beer at 5% ABV and you added 1 quart of "80 proof" spirits, how would one calculate the resulting ABV?

• US gallons or imperial gallons? – Pharap Sep 7 '14 at 0:32
• Added "US" to question. – Dale Sep 8 '14 at 22:29

This seems like a simple solution dilution problem. Take

``````5 gallons = 20 quarts => 20 quarts * 5% ABV = 1 quart alcohol.
``````

Then take your 1 quart of "80 proof" (40% ABV), and we get

``````1 quart * 0.4 = 0.4 quarts alcohol
``````

So we have a total volume of 21 quarts (beer plus spirits) and a total of 1.4 quarts alcohol, thus

``````1.4 / 21 = 6.67% ABV
``````

Unless I'm missing something about ABV percentage, `6.67%` should be the final answer.

In general, if we have (making sure we are using consistent units)

``````O - the original volume, in quarts
A - the volume of spirits to add, in quarts
s - the % ABV of the original volume
p - the % ABV of the spirits
``````

Then we can use the general formula below

``````((O * s) + (A * p)) / (O + A)
``````
• Is that a US gallon or an imperial gallon? – Pharap Sep 5 '14 at 23:48
• US gallon, but the idea is the same, get the total alcohol in each fluid, and combine – CDspace Sep 6 '14 at 0:33
• Just clarifying since these differences can cause issues sometimes. (For instance 40% ABV is 80 proof in the US but 40% ABV in the UK is 70 proof.) I should have realised though that it's a matter of ratio the units in use are slightly irrelevant. – Pharap Sep 7 '14 at 0:53
• @pharap Indeed, this type of problem is a basic homework problem in university physics 1. The units don't matter as much as the method. – CDspace Sep 7 '14 at 0:55
• @dale that would probably work better as a separate question. I'm not really sure how that might be done – CDspace Sep 13 '14 at 16:36