Real Extract (RE) is a precise calculation concerning the gravity of beer. It is related to a boiled wort’s gravity, a fermented wort’s attenuation, and a finished beer’s alcohol level. The specific gravity of wort—its density—is greater than that of water, which sets the mark at 1.000 because of the presence of sugars in solution. Gravity is commonly measured in terms of original gravity or degrees Plato (°P). See original gravity and plato gravity scale. A standard beer may have an original gravity of 1.048 or 12°P. As beer is being fermented—or attenuated—its gravity decreases because sugars are converted into carbon dioxide gas, which largely escapes, and alcohol, mostly ethanol, which mostly stays in the beer.

Attenuation is thus the extent to which wort sugar has been converted to alcohol. If a beer has plenty of residual sugar after fermentation, it has a lower attenuation value than a beer from the same-gravity wort with next to no residual sugars. If the difference in gravity between the starting wort and the finished beer is measured using a hydrometer, this attenuation value is misleading, because the wort gravity is measured based on sugar dissolved in a reference liquid of water only. The beer gravity is measured based on residual sugars dissolved in a reference liquid that is both water and alcohol. This is significant, because alcohol has a lower density (or gravity) than water. Thus, the difference between the hydrometer readings of wort gravity and of finished beer gravity lead to a value called apparent attenuation—“apparent” rather than actual, because it contains a small error. See attenuation and hydrometer.

That error is based on ethanol having only 79% of the gravity of pure water. RE, therefore, is the corrected value for the amount of attenuation. It is derived mathematically from the initial wort gravity and the final beer gravity, both measured in °P, with two correction factors. RE, therefore, takes into account the effect of the presence of alcohol in the finished beer (and the absence of alcohol in the starting wort). The formula for determining RE is (with 0.1808 and 0.8192, respectively, as correction constants)$Display mathematics$.

If the original gravity of a wort is 1.048 (or 12°P), for example, and the finishing gravity of the beer is 1.012 (or 3°P)—these are two are very common values in average session beers—using a rounded value of 4 gravity points equal 1°P, RE is$Display mathematics$