It never hurts to have
another hydrometer on hand!
The amount of alcohol in your beer is determined by measuring your original gravity prior to fermentation, then your final gravity after fermentation is complete. Unless you add other fermentables (most often, fruit or additional sugars) after you take your original gravity reading - which have to be accounted for on their own - you can simply use these two number to calculate the amount of alcohol by volume. This is due to the fact that alcohol is less dense than water; therefore, as your wort ferments (and the sugars are converted to alcohol), the density of the beer decreases.
The basic formula used by most homebrewers is pretty simple: ABV = (OG - FG) * 131.25.
ABV = alcohol by volume, OG = original gravity, and FG = final gravity. So, using this formula with a beer having an OG of 1.055 and a FG of 1.015, your ABV would be 5.25%.
There is one caveat - this formula only yields an approximate ABV. In actuality, the formula becomes less precise as alcohol levels increase. There is a more precise way to figure your alcohol content, but it requires quite a bit of math to do so, unless you already have an accurate alcohol by weight measurement.
ABV = (ABW * (FG / .794) )
Where ABW is alcohol by weight. To get alcohol by weight, you must know that original extract value (which is figured from the orignal gravity of the beer) and the real extract value (which is figured from apparent extract, which in turn is figured from the measured final gravity of your beer, as well as the atteunation coeeficient, which is figured from the original extract number). Extract, incidentally, is measured in degrees Plato.
That formula, if you care, follows.
ABW = (OE - RE) / (2.0665 - (.010665 * OE) )
Using our sample beer above (OG 1.055, FG 1.015), we find that our simple formula was actually quite accurate - we get a rounded value of 5.25%.
The differences between the two formulae does, however, grow greater as the alcohol content grows. Let's use a bigger beer as a second example. This one has an OG of 1.086, and a FG of 1.019.
With the simple formula, we get an ABV of 8.79%. With the more complex formula, we get a measurement of 8.87%
A third example is a barleywine with an OG of 1.120 and a FG of 1.030.
The simple formula gives us an ABV of 11.81%. The more complex formula gives us a mark of 12.05% ABV for this massive beer.
The precision level of the calculation may or may not matter to you; many homebrewers use an even simpler version than the simple formula above (ABV = (OG - FG) * 131), and figure that it is close enough. That being said, you might find this little calculator to be useful or enjoyable... and if nothing else, non-math whizzes should find it to be a lot easier than trying to use the more complex formula.
Credit for the math goes to Dr. Michael Hall, in his article entitled "Brew by the Numbers - Add up What's in Your Beer" (Zymurgy, summer 1995). Special thanks also go out to BYO magazine, Beersmith, and assorted internet blogs that I used for fact checking and confirming formula content.