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The numbers explained
Craft Beer Introduction October 20, 2005
Written by xray

Bloomfield, NEW JERSEY -

Whether you are a homebrewer and would like to know how much alcohol is in your beer, or you would like to know how to convert alcohol by weight (ABW) to alcohol by volume (ABV) or vice versa, the formulas are contained below.

The first pieces of information we need are a beer’s Specific Gravity (SG) during different stages of the beer making process. The SG of a liquid (or anything) is the measure of density that a liquid has as compared to water at 4°C. The SG of water at 4°C (the temperature at which water is densest) has been designated as having a SG of 1 because…well, just because. So if a gallon of a mystery liquid weighs half as much as a gallon of water, its SG is 0.5. The two SGs we’re concerned with are the Original Gravity (OG) and the Final Gravity (FG) - also called Terminal Gravity (TG).

The OG of a beer, is the SG a beer has before it becomes a beer (while it is still a wort). Since wort is basically water with dissolved sugars in it (mostly glucose), and glucose is denser than water, the SG of a wort is always more than 1.

The FG of a beer is the SG once it is fermented and we can call it beer. Since yeast added to the wort has converted some of the sugars in to alcohol and CO2 (both less dense than water), the FG will always be less than the OG.

Once we have the measurements of a beer’s OG and FG, we can determine its ABW. Let’s use a beer with a OG of 1.044 and a FG of 1.007 as an example. Take the beer’s FG and subtract it from the beer’s OG. Most of the weight difference between the two is from CO2 bubbling off ( 0.037 k/l in this case ). We then take 0.037 and multiply by 1.05 (because for every gram of CO2 that has bubbled away, 1.05 grams of alcohol are produced). 0.03885 kg/l is the weight of the alcohol that has been produced. Dividing the the weight of the alcohol (0.03885) by the FG (1.007), we get the ABW (3.87%).

Summary: 1.044 - 1.007 = 0.037

0.037 x 1.05 = 0.03885

0.03885 ÷ 1.007 = 0.0386 = 3.86% ABW

To convert ABW to ABV we take our ABW and divide by the density of ethyl alcohol (0.79). Ex. 3.86% ABW ÷ 0.79 = 4.89% ABV

To convert ABV to ABW simply multiply ABV and 0.79. Ex. 4.89% ABV x 0.79 = 3.86% ABW
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