Abv

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No it should not. Your ABV is calculated from your starting SG and ending SG before sweetening. I use (starting SG - ending SG) x 131.25 for ABV. Make sure you add sorbate before back sweetening or fermentation will resume, and ABV will be inaccurare.
 
If you back sweeten the wine, does this affect the final ABV?


Yes, because the volume is increasing and the amount of alcohol is staying the same.

For example if you have 1gal of 10% alcohol (1.6c alcohol) and add 1c of inverted sugar liquid, then you have 1.6/17 or ~9.412% alcohol.

Or if you are removing 1c of the wine to add the 1c sugar, it would be 1.5/16 or 9.375% alcohol.

Or with 15% alcohol, that would be 2.4/17 or ~14.12%, or removing the cup, would give you: 14.0625%

So its safe to say 1cup of back sweetening per gallon will likely lower the ABV any where from 3/5ths of a % to almost 1 full %.
 
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