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Alcohol content of beer is determined by the amount of fermentable sugar that is converted by yeast into alcohol. There are several variables in the fermentation process that can effect the alcohol content of your beer. Starch is converted into fermentable sugar during the mash process, and the amount of fermentable sugar in the wort determines the potential alcohol content of the beer. This potential (the amount of fermentable sugar in the wort) can be measured in terms of specific gravity and is called the "original gravity" of the beer. In extract kits it is predetermined by the maker of the extract syrup or powder, according to the recipe of the beer. Of course, you can increase the amount of available fermentable sugar in any recipe by adding more extract or sugar, but normally a kit is designed to fall into a narrow range of alcohol content, most around 4.5-5% ABV.
The second variable in the fermentation process is the yeast's ability to convert fermentable sugar into alcohol. Some yeast strains are able to survive environments (your fermenter) that contain high levels of alcohol, others will perish when the alcohol content exceeds a certain potency. Yeast's ability to convert fermentable sugar into alcohol varies by strain and temperature range as well. "Attenuation" is the term used to describe how thoroughly a strain of yeast will convert fermentable sugar, within a prescribed temperature range. Ale yeast strains normally convert at temperature ranges of 65-75 deg F. Lager strains convert at ranges of 45-60 deg F, but more slowly than ale yeasts.
Fermentation must take place in a controlled environment. Temperature swings of more than a few degrees can cause undesirable flavors to be present in the beer, or cause the yeast to stop converting sugars altogether. In pilsner type beers, the temperature of the beer is lowered when a predetermined specific gravity is reached in order to "crash" the yeast, which causes fermentation to cease. This limits the alcohol content of the beer to specific levels. Of note, yeast must be "viable" (healthy and pure), oxygen must initially be present for the yeast to establish a colony that can convert the fermentable sugar, and no foreign bacteria can be present which could compete with the yeast. When fermentation has completed, another specific gravity measurement should be taken, termed "final gravity". The difference between the original gravity and the final gravity of the beer is directly proportional to the alcohol content by volume.
There are ranges of alcohol content by volume that are traditionally associated with specific types of beers. You can learn more about these beer "styles" in books or by asking your local homebrew supplier (and perhaps, even on this website, or others like it). One beer style, for example, a pilsner, should contain approximately 4-5% ABV, while other beer styles, like India Pale Ales, call for higher alcohol content, 6-7% ABV. German Doppelbocks are defined by their original gravities, which must exceed 1.048.