# Calculation - ABV

### ABV is an abbreviation for alcohol by volume.

This unit is a standard measure of how much alcohol (ethanol) is contained in a given volume of an alcoholic beverage. It is expressed as a percentage of the total volume. Meaning, this is the number of millilitres (ml) of pure ethanol present in 100 mL of a solution at 20°C (68°F). The ABV standard is commonly used worldwide. In some countries, e.g. France, the term alcohol by volume is often replaced by degrees Gay-Lussac (thanks to the French chemist Joseph Louis Gay-Loussac). These two scales differ slightly: Gay-Lussac uses the value of 15°C (59 °F) for temperature (instead of 20°C).

To estimate ABV, we use the gravity of the beer. Gravity refers to the density of the solution. In wort, we are dealing with two items contributing to the overall density of the solution. The first is water, which makes up greater than 90% of the solution, which has a density of 1.000, and the second is sugar from the malt. Sugar is a larger heavier molecule than water, and, therefore, when sugar is dissolved in water, the density of water is increased. In finished beer, there is a third contributor, ethanol produced by the yeast. Ethanol is lighter than water with a density of 0.789. Therefore during fermentation, the sugar is consumed, and ethanol is produced, lowering the overall density of the solution. The Original Gravity (OG) refers to the gravity of the wort pre-fermentation, and the Final Gravity (FG) refers to the Gravity post-fermentation. For more on the calculation of OG and FG, please see the OG & FG calculation document (add hyperlink).

The Simples formula used by homebrewers is the “Standard”:

This equation is so old it is challenging to find the original reference but one reference that uses this method is the joy of homebrewing by Charlie Papazion (Papazian, September, 2014). This method uses the difference between the final gravity and the original gravity, multiplied by a constant to get ABV. The Constant of 131.25 in the equation comes from two different factors:

- 1.05 accounts for the number of grams of ethanol generated per gram of carbon dioxide released in fermentation.
- 0.80 represents the approximate density of ethanol, which is necessary to convert from alcohol by weight (ABW) to alcohol by volume (ABV).

To understand the first factor, we consider the fermentation glucose following the balanced chemical equation below:

This equation shows us that for every carbon dioxide molecule released during fermentation, an ethanol molecule is produced. Since the molar mass of ethanol is 46.07 g/ml compared to 44.01 for carbon dioxide, approximately 1.05 g of ethanol will be generated for every 1.00 gram of CO2 (46.07/44.01 = 1.04681 ≈ 1.05).

Next, we have to consider the physical significance of subtracting the final gravity from the original gravity (OG-FG). Specific gravity measures, the density of a solution relative to that of some reference substance (in most cases, water). So why does the gravity reading change over the course of fermentation? The answer to this can be thought of as fermentable sugars in the wort are being consumed by yeast and converted to ethanol (which has a lower density than water) and carbon dioxide (which is mostly lost to the atmosphere out the airlock). The relationship between a change in specific gravity and the ABV produced is not linear. As a result, larger deviations in the change in SG and ABV are observed for higher gravity beers. Therefore, different multipliers and more sophisticated equations can be used to get closer to the actual ABV in those cases, which we will cover later.

A scenario where the specific gravity drops from 1.050 to 1.010 at the end of the fermentation. In this case, OG-FG = 0.040. The first approximation is that gravity loss can be contributed to CO_{2} escaping out the airlock. Remembering the density of water is 1.00 g/mL, this results as a loss of 0.040 g of CO_{2} per mL of solution (beer). We can now put this all together to solve for ABV:

The first step above translates CO2 lost to mass ethanol produced using the first factor. The next conversion uses the* approximate* density of ethanol (the second factor, 0.80 g/mL) to relate ABW to ABV. The factor of 100 is needed to express the final value in a percentage. Putting it all together, you have (OG-FG) x 1.05 100/0.8, which simplifies to the equation to (OG-FG) x 131 = ABV.

The Next is the common “Alternative” Formula is from Micheal Hall’s Zymergy article in January 1995. Unfortunately we could not get access to to the article. It looks like this is based on the Balling equation:

There are two assumptions the Balling equation makes.

- The first assumption is that 0.11 g of carbohydrate (sugar) is converted to yeast mass for each gram of ethanol produced in fermentation.
- The second assumption is that all fermentable dissolved wort solids are monosaccharides. This assumption is implicit in the composition of the Balling constant.

The most recent formula was derived by Cutaia, Reid and Speers in 2009 by challenging the assumptions made from the Balling equation. The first formula from their research relates the measurements of the alcohol content by weight (ABW) percentage with the Original (OE)(OG) and Apparent extract (AE)(FG) measured in ^{˚}P (Anthony J. Cutaia, 2009):

Remembering the relationship between alcohol & carbon dioxide produced and the reduction of density is not linear but potentially polynumberal and from ABW formula, they derived an equation for alcohol by volume (Anthony J. Cutaia, 2009):

Graph is based on an FG of 1.010 (2.5˚P) and based on the conversion equation:

Remembering that all formulas for calculating the ABV are approximations, as they can only be proved by chemical analysis of the final beer. But from this data we can see that the three equations result in very similar ABVs until the OG reaches 1.050 (12.5˚P). The equations then start to diverge until there is an ~1.5% ABV difference between the three calculation methods at the high end. Here at Grainfather the standard option is used however in the preferences section of you settings you can set the calculation to the Alternative or the Cutaia equations.

#### References

Anthony J. Cutaia, A.-J. R. (2009). Examination of the Relationships Between Original, Real and Apparent Extracts, and Alcohol in Pilot Plant and Commercially Produced Beers. *Journal Of the institute of Brewing *, 318-327.

Fix, G. (1999). *Principles of Brewing Science 2nd Ed.* Brewers Publications.

Papazian, C. (September, 2014). *The Complete Joy of homebrewing.* William Morrow Paperbacks.