Need help calculating ABV after adding distilled alcohol to beer

General Homebrew Discussion
1

Let’s say I have 16 oz of 7% ABV home brew. I add 1 oz of 40% distilled spirits to it… What formula is used to figure the new ABV?

2

Since percentages scale linearly, you can just add them proportionally:

((167)+(140))/(16 + 1) = 8.94% ABV

Edit: It works for any other linear relationship too: specific gravity, IBU, etc.

Edit 2: I really shouldn’t try to do things in my head (I divided by 8 instead of 17). Thanks, Drew.

3

That seems off to me… Thinking about it this way:

16 oz of 7% abv = 1.12 oz of ethanol in the pint
1 oz of 40% abv = 0.4 oz of ethanol

So you now have 1.52 oz of ethanol in 17oz of fluid (assuming perfect mixing etc)

1.52 / 17 = 0.089 = 8.9%