The easy way to figure out ABV is to convert the ABV of the vodka to a decimal (so 60% ABV = 0.6) and multiply the ABV decimal by the total volume of liquid. (Keep in mind most bottles list proof which is double the ABV. So a 120 proof vodka is 60% ABV.) The equation is ABV of vodka x (volume of vodka + volume of water).

For example 1 oz of 60% vodka plus 11 oz water gives you 12 oz of liquid. You calculate ABV as 0.6 x 12 oz = 0.05 or 5% ABV.

That happens to work for the example cited. Putting 2oz of spirit in with 11oz of water, however, should result in 9.2% ABV, and the above method gives 7.8%.

Actual calculation

Finished ABV = (ABV of spirit * VOL of spirit) / (VOL of spirit + VOL of water)

The numerator is the volume of pure alcohol, the denominator is the total volume of the mixture.

Ex:

Finished ABV= (0.60*1L)/(1L+11L) = 0.60/12 = 0.05

Ex 2:

Finished ABV = (0.60*2L)/(2L+11L) = 1.2/13 = .092

Probably a more useful equation is how much booze do you need to make a specified volume at a specified ABV...

Vol Spirit =(ABV desired * Vol desired) / ABV Spirit

Ex:

Vol Spirit = (0.05 * 5 gallons) / 0.60 = .42 gallons (or 1.6L)