Until the invention of the beer hydrometer, brewing entailed more trial and error than it does today. For example, it was not always readily apparent when fermentation was complete, and it was next to impossible to determine alcohol content. A beer hydrometer assists on both of these fronts. Anyone interested in home brewing would be well advised to invest in one. They are not very expensive and are very easy to use properly.
Put simply, a hydrometer measures the density of liquid. For brewers, the hydrometer tells them the amount of fermentable sugars dissolved in their wort (unfermented beer). By measuring the density of the beer before and after fermentation, the brewer is able to determine when fermentation is complete and how much sugar was converted into alcohol.
The most common kind of beer hydrometer is the so-called triple scale hydrometer. This is because it can provide three different measurements: specific gravity, potential alcohol, and the balling scale. The reading most commonly used by home brewers is specific gravity, so this will be addressed in more detail.
Specific gravity is a measure of the density of a liquid compared to water at 60 degrees Fahrenheit. As a baseline, water is considered to have a specific gravity of 1.000. When fermentable sugars and other ingredients are dissolved in water, the specific gravity rises. For example, one gallon of water with one pound of malt extract dissolved in it will have a specific gravity of about 1.040. As fermentation proceeds, the specific gravity will decrease as yeast converts the sugars from the malt into alcohol and carbon dioxide.
Using a beer hydrometer is very simple. The hydrometer itself is a glass cylinder that is stored in a plastic tube. Before adding yeast to the wort, a small sample of the wort is poured into the tube. Make sure the hydrometer is floating freely, and then read where the level of the liquid is on the scale.
Since most beer hydrometers are calibrated to read accurately at 60 degrees, for every ten degrees above that, add .002-.003 to the result. Your result is known as the original gravity. Once fermentation appears to be over, draw off another sample and take another reading. Do this again in a day or two. After two or three successive readings show no change, fermentation is complete. To determine alcohol content, subtract the final gravity from the original gravity, ignoring the decimal point. Multiply the result by .1275. For example, if the original gravity is 1.040, and the final gravity is 1.010, then 1040-1010=30. 30x.1275=3.825% alcohol by volume.