I sometimes make alcoholic ginger beer and alcoholic lemonade. How would one estimate the abv of something like that? Is it even possible?
Yup, it can be easily measured using a hydrometer. Simply take a specific gravity reading before pitching yeast and after fermentation is complete. Find the difference between the two values, this will be proportional to the amount of sugar the yeast has converted to alcohol. Multiply this number by 131 and you get the ABV. For example:
You brew a ginger beer with original gravity (OG) of 1.09. After fermentation the final gravity (FG) is 1.01. The alcohol by volume is as follows:
ABV = (OG - FG)*131 = (1.09-1.01)*131 = .08*131 = 10.48%
Alternatively, if you don't have a hydrometer, you can make some educated guesses. If you know about how much sugar you are have, you can estimate the starting gravity using the specific gravity yield of the kind of sugar you are using.
I could go over the math for this, but if you want to make it easy on yourself, just use Beer Calculus. Just add your ingredients and it will estimate OG, FG, and ABV.