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'Original gravity' (OG) usually refers to the density of wort, unfermented beer, usually expressed as a ratio to the density of water (thus for instance 1.050, occasionally expressed 1050). The density is closely related to the amount of fermentable sugar dissolved in the wort, and thus predicts the likely strength of the finished beer.
'Final gravity' (FG) is the density of the beer once the fermentation has finished. The difference between OG and FG is a measure of the amount of sugar consumed in the fermentation, and therefore of the alcohol evolved. Different yeasts have different powers of attenuation (ability to consume wort sugars), and different worts may have higher or lower proportions of non-fermentable sugars, so final gravity is not a simple function of original gravity.
The main reason the density drops during fermentation is that the process breaks down sugar molecules into ethanol and carbon dioxide, the majority of the latter escaping as gas. Ethanol at 790 kg/m³ is less dense than water's 1000 kg/m³.
Brewers record OG readings with a hydrometer after cooling the wort to a reference temperature (usually about 15°C). After fermentation is complete, a FG reading is taken to compare the relative densities of the beginning solution and the finished product. Because liquids are less dense at higher temperatures, it is important to take the initial reading at the same temperature as the final reading.
An approximate calculation gives the percent alcohol by volume as a function of the original and final gravities as follows:
:, for example