During the production of wine and beer,
yeast is added to a sugary solution. During fermentation, the yeasts consume the sugars and produce alcohol. The density of sugar in water is greater than the density of alcohol in water. A
hydrometer is used to measure the change in
specific gravity (SG) of the solution before and after fermentation. The volume of alcohol in the solution can then be estimated. There are a number of empirical formulae which brewers and winemakers use to estimate the alcohol content of the liquor made. Specific gravity is the density of a liquid relative to that of water, i.e., if the density of the liquid is 1.05 times that of water, it has a specific gravity of 1.05. In UK brewing usage, it is customary to regard the reference value for water to be 1000, so the specific gravity of the same example beer would be quoted as 1050. The formulas here assume that the former definition is used for specific gravity.
General During
ethanol fermentation the yeast converts one
mole of sugar into two moles of alcohol. A general formula for calculating the resulting alcohol concentration by volume can be written: :ABV = SBV fermented \times GECF where SBV fermented is sugar by volume (g/dL) converted to alcohol during fermentation and GECF is the glucose-ethanol conversion factor: :GECF = \frac{2 \times 46.069}{180.156} \approx 0.511435 where 46.069 is the
molar mass of
ethanol and 180.156 is the molar mass of
glucose and
fructose. :ABV \approx SBV fermented \times 0.511435 :SBV fermented = SBV start - SBV final Sugar by volume can be calculated from
Brix (sugar by weight) and SG (relative density): :SBV = Brix \times SG SG can be measured using an
hydrometer and Brix can be calculated from SG. A simple formula for calculating
Brix from SG is (SG 1.000 - 1.179): :Brix = 263.663 - \frac{263.806}{SG} By substituting Brix in the SBV formula above, we get a formula for calculating SBV from SG only: :\text{SBV} = 263.663 \times SG - 263.806 By further substitution, we get a formula for calculating ABV from SG only: :SG drop = SG start - SG final :SBV fermented = 263.663 \times SG drop :ABV \approx 263.663 \times 0.511435 \times SG drop \approx 135 \times SG drop SG drop is how much the SG decreased during fermentation (at 20 degree C). The factor 135 is most accurate in the center of the SG drop range of 0.000 to 0.179. Since the correlation of SG and Brix is non-linear it is common to divide the range to increase accuracy when using the simple ABV formula: :ABV \approx factor \times SG drop Example ABV calculation: • SG measured at start of fermentation 1.067 • SG measured at end of fermentation 1.007 • SG drop = 1.067 - 1.007 = 0.06 • Factor from table above 134 • ABV = 134 x 0.06 = 8.04
Advanced Advanced formula derived from Carl Balling empirical formulas. The formula compensates for changes in SG with changes in alcohol concentration and for the fact that not all sugar is converted into alcohol. All values are measured at 20 degree C. ABV = \frac{-118772 \times \text{SG final} \times (\text{Plato start} - \text{Plato final})}{(\text{Plato start} - 193.765) \times (\text{Plato start} + 1220)} where SG final is the specific gravity when fermentation ends, Plato start is the sugar by weight when fermentation begins, Plato final is the sugar by weight when fermentation ends.
Brix can be used instead of Plato as they are nearly identical.
Wine The simplest method for wine has been described by English author
Cyril Berry: \text{ABV} \approx 136 \times \left( \text{Starting SG} - \text{Final SG} \right)
Beer One calculation for beer is: \text{ABV} \approx 131 \times \left( \text{Starting SG} - \text{Final SG} \right) For higher ABV above 6% many brewers use this formula: \text{ABV} \approx \frac{105}{0.79} \times \left( \frac{\text{Starting SG} - \text{Final SG}}{\text{Final SG}} \right) \approx 132.9 \times \left( \frac{\text{Starting SG} - \text{Final SG}}{\text{Final SG}} \right) ==Other methods of specifying alcohol content==