Formula to calculate alcohol % after a bourbon addition?

I should be able to figure this out, but for some reason my brain isn't working today (too much bourbon last night perhaps?).

Anyway, I recently made a bourbon porter similar to the popular vanilla bourbon porter recipe floating around, and I wanted to correctly calculate the ABV after my bourbon addition.

If I have 5 gallons of porter @ 6.7% ABV and add 10oz of bourbon at 45% abv, how many points does that raise the 5 gallons? What is the formula to calculate this?

 

A little trial and error with this calculator shows 0.7% uplift in ABV diluting 10oz of 45% spirits in 5 gallons of water.

 

I just did the following:

(Beer Volume (in oz) * Beer ABV %) + (Bourbon Volume (in oz) * Bourbon ABV %) / (Beer Volume + Bourbon Volume)

So,

(640*.067) + (10*.45) / (640 + 10) = .073, or 7.3 % alcohol. That sounds about right I think.. hopefully my method is correct.

 

I did it by hand and came up with about the same. Resulted in 7.3% ABV (off by .1 from the calculator above, could just be rounding?). Just for fun, let me know if I'm missing something here:

5gal=640 ounces. 640(.067)=42.88 alc oz.
10oz(.045)= 4.5 alc oz.
42.88+4.5=47.38
new volume yield = 650 ounces
650(x)=47.38 alc oz.
x=.07289
~7.3%

edit: looks like someone does math a bit faster than me! Same results though which is nice to see!

 

Simple dilution. M1V1 = M2V2

 

its right as long as your original ABV wasn't based on a FG after the bourbon was added since it'll lower it

 

Yep it was based on a FG BEFORE the addition of the bourbon. This beer tastes fantastic BTW and is hands-down, the best one I've ever brewed.