determine ABV when diluting

Is this the right way to figure out ABV when diluting?
I know I will have to sulfite, sorbate and force carb, and this may not be the sweetening dilution percentage used. But I found that sweetening with juice taste a lot better than sweetening with concentrate. I just want to have an idea how much ABV is in my final product.

Let’s say I have a 5 gallon (640 oz.) batch of cider with OG of 1.062 and FG of .996, the ABV would be 8.646%.
Calculation --> (1.062 - .996) * 131 = 8.646

8.646% of 5 gallons (640 oz.) is 55.3344 oz. of pure alcohol.
Calculation --> 640 * .08646 = 55.3344

If I sweeten with 1 gallon (128 oz.) apple juice to make a total of 6 gallons (768 oz.) the pure alcohol would still be 55.3344 oz., making the ABV 7.205%.
Calculation --> 55.3344 / 768 = 7.205

Is this correct?

What is the SG of the juice? There is a dilution tool in beersmith where you can dilute with wort and it will give you an adjusted FG so you can determine the ABV.

I did a quick google search and found one person that said apple juice SG was somewhere around 1.040, so if you add 1 gal of 1.040 juice to 5 gal of 1.062, beersmith says that raises the FG from .996 to 1.003, so your new ABV would be 7.729%

drunkatuw said:

What is the SG of the juice? There is a dilution tool in beersmith where you can dilute with wort and it will give you an adjusted FG so you can determine the ABV.

I did a quick google search and found one person that said apple juice SG was somewhere around 1.040, so if you add 1 gal of 1.040 juice to 5 gal of 1.062, beersmith says that raises the FG from .996 to 1.003, so your new ABV would be 7.729%

Click to expand...

Thanks, I don't have time now but I'll check it out later, The juice is 1.050 (Mott's). It looks like I am in the ballpark atleast but your way may be simpler.

drunkatuw said:

What is the SG of the juice? There is a dilution tool in beersmith where you can dilute with wort and it will give you an adjusted FG so you can determine the ABV.

I did a quick google search and found one person that said apple juice SG was somewhere around 1.040, so if you add 1 gal of 1.040 juice to 5 gal of 1.062, beersmith says that raises the FG from .996 to 1.003, so your new ABV would be 7.729%

Click to expand...

BUT, this is not being fermented, so that doesn't change the ABV at all. You're adding juice to alcohol, which is the same as adding water as far as dilution is concerned. What I'm saying is- if you have 5 gallons of 8.6 % ABV, and you add a gallon of anything that isn't going to be fermented, you'll have 6 gallons instead of 5. So, using the dilution tool in Beersmith, that would give you 6 gallons of 7.3% liquid. (Which matches your calculation, but is easier).

I had a really bad Physics 1 Prof in college but I remember this formula:

C1V1 = C2V2

It's quite useful in brewing. C = Concentration and V = Volume. The 1s and 2s are supposed to be subscripted. You can use any units you want as long as they're the same on both sides of the equation. This won't account for your newly added alcohol that the 1 gallon of applejuice would add though. Sounds like drunkatuw got that one for you.

EDIT: Woops, Yooper said the new applejuice isn't being fermented:cross:, so you can use that formula to get the same answer you got in your OP.

OK, I just tried to install a trial version of beersmith and it says trial expired. so I guess I can't use it unless I buy it. As Yooper said the newly added juice will not be fermented, it will be added for flavor and sweetning instead of adding concentrate. my calculations where off by .10 which is barely anything. All I was looking for was a ballpark figure and the responses here have confirmed my calculations. Thanks for your help.

Edit: I just found a dilution calculator.
http://www.homedistiller.org/dilute.htm
This calculates the opposite way, but if you enter 5 gal and ABV from 8.646 to 7.205 which are the numbers I came up with, you get 1 gallon.
Now I'll just make a calculator on excel and I'm all set.