Alcohol by volume

In some countries, e.g. France, alcohol by volume is often referred to as degrees Gay-Lussac (after the French chemist Joseph Louis Gay-Lussac), although there is a slight difference since the Gay-Lussac convention uses the International Standard Atmosphere value for temperature, 15 °C (59 °F).

Volume change

Mixing two solutions of alcohol of different strengths usually causes a change in volume. Mixing pure water with a solution less than 24% by mass causes a slight increase in total volume, whereas the mixing of two solutions above 24% causes a decrease in volume. The phenomenon of volume changes due to mixing dissimilar solutions is called "partial molar volume". Water and ethanol are both polar solvents. When water is added to ethanol, the smaller water molecules are attracted to the ethanol's hydroxyl group, and each molecule alters the polarity field of the other. The attraction allows closer spacing between molecules than is usually found in non-polar mixtures.

Thus, alc/vol is not the same as volume fraction expressed as a percentage. Volume fraction, which is widely used in chemistry (commonly denoted as v/v), is defined as the volume of a particular component divided by the sum of all components in the mixture when they are measured separately. For example, to make 100 mL of 50% alc/vol ethanol solution, water would be added to 50 mL of ethanol to make up exactly 100 mL. Whereas to make a 50% v/v ethanol solution, 50 mL of ethanol and 50 mL of water could be mixed but the resulting volume of solution will measure less than 100 mL due to the change of volume on mixing, and will contain a higher concentration of ethanol. The difference is not large, with the maximum difference being less than 2.5%, and less than 0.5% difference for concentrations under 20%.

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Threshold levels

Legal thresholds

Some drinks have requirements of alcoholic content in order to be certified as a certain alcohol brand or label. For example, in the United Kingdom, the United States, Canada and European Union whisky is legally required to be no less than 40% ABV bottled.

Low-alcohol beers (<0.5) are considered in some countries such as Iran as permitted (halal) despite alcohol being banned. However, the level of alcohol-free beers is typically the lowest commercially sold 0.05.

Biological thresholds

It is near impossible for a healthy person to become intoxicated drinking low-alcohol drinks. The low concentration severely limits the rate of intake, which is easily dispatched by human metabolism. Quickly drinking 1.5 L of 0.4% alc/vol beer in an hour resulted in a maximum of 0.0056% BAC in a study of German volunteers. Healthy human kidneys can only excrete 0.8–1.0 L of water per hour, making water intoxication likely to set in before any alcoholic intoxication.

The process of ethanol fermentation will slow down and eventually come to a halt as the alcohol produced becomes too concentrated for the yeast to tolerate, defining an upper limit of alc/vol for non-distilled alcoholic drinks. The typical tolerance for beer yeasts is at 8–12%, while wine yeasts typically range from 14–18%, with speciality ones reaching 20% alc/vol. Any higher would require distillation, producing liquor.

Typical levels

Details about typical amounts of alcohol contained in various beverages can be found in the articles about them.

Practical estimation of alcohol content

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:

A B V = S B V f e r m e n t e d \times G E C F

where SBV fermented is sugar by volume (g/dL) converted to alcohol during fermentation and GECF is the glucose-ethanol conversion factor:

G E C F = \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.

A B V \approx S B V f e r m e n t e d \times 0.511435

S B V f e r m e n t e d = S B V s t a r t - S B V f i n a l

Sugar by volume can be calculated from Brix (sugar by weight) and SG (relative density):

S B V = B r i x \times S G

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):

B r i x = 263.663 - \frac{263.806}{S G}

By substituting Brix in the SBV formula above, we get a formula for calculating SBV from SG only:

SBV = 263.663 \times S G - 263.806

By further substitution, we get a formula for calculating ABV from SG only:

S G d r o p = S G s t a r t - S G f i n a l

S B V f e r m e n t e d = 263.663 \times S G d r o p

A B V \approx 263.663 \times 0.511435 \times S G d r o p \approx 135 \times S G d r o p

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:

A B V \approx f a c t o r \times S G d r o p

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.

$A B V = \frac{- 118772 \times SG final \times (Plato start - Plato final)}{(Plato start - 193.765) \times (Plato start + 1220)}$

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:

$ABV \approx 136 \times (Starting SG - Final SG)$

Beer

One calculation for beer is:

$ABV \approx 131 \times (Starting SG - Final SG)$

For higher ABV above 6% many brewers use this formula:

$ABV \approx \frac{105}{0.79} \times (\frac{Starting SG - Final SG}{Final SG}) \approx 132.9 \times (\frac{Starting SG - Final SG}{Final SG})$