New Gravity after adding Sweetners

What's the procedure for calculating alcohol content after adding additional sweetners? I fermented a batch of Apfelwein, and in order to make it into something my mom would drink, I had to add a bunch of frozen apple juice concentrate. I added about 6 large cans of concentrate and then one additional cup of corn sugar to my 3-gallon batch of Apfelwein.

My original gravity before fermentation was 1.062.
My gravity after fermentation was 0.996.

At this point, I added potassium sorbate to stop any additional fermentation.

I added 6 cans of apple juice concentrate plus 1 cup of corn sugar.

My new gravity at this point is 1.032.

If I figure the alcohol by volume based on the difference between 1.062 and 1.032, it comes up to 3.9%, which may be accurate, but it doesn't seem like it would be accurate since I only added less than 1/2 gallon of content to the 3-gallon batch...

No, you figure the ABV by OG-FG and then multipling it by .131 or so. (1.062-.996) x .131 = approx 8.6% ABV

Sweetening (or not sweetening) doesn't change the ABV, since it doesn't ferment out and increase the alcohol content.

Since you added 1/2 gallon (diluted it), though, that's not entirely accurate. You could figure out the dilution, if you knew the exact amount you added.

Double Post

You didn't affect how much ethanol you created by backsweetening. So you would calculate your abv by (1.062-.996)*131 = 8.646%

If you want to be precise though, that would be for your initial volume prior to backsweetening. So your new abv would be .08646(X initial Volume) = Y new %(Initial Volume + backsweetening volume) plug in your volumes and calculate your Y new abv %

If you're considering 1.032 your FG, your OG is actually 1.062 + (1.032 - 0.996) = 1.098. Of course that is just a lot of work for nothing, since you end up at the same place... 8.646% ABV. To calculate the change in ABV by adding water:

(original volume * alcohol percentage) / new volume

if you added half a gallon:
3 * 0.0846 / 3.5 = 7.41% ABV

Thanks everyone... This solves the problem