If I get a beer labelled 5% ABV, how accurate is that measurement likely to be?
tl;dr — By regulation, ±0.3-0.5%.
Chemically speaking, I'm not sure—maybe someone else can go into measuring techniques, alterations (continued fermentation?) during distribution, etc.
But countries and regions specify tolerances for error.
In the United States, according to Title 27: Alcohol, Tobacco, and Firearms, Part 7: Labeling and Advertising of Malt Beverages, §7.71:
(c) Tolerances. (1) For malt beverages containing 0.5 percent or more alcohol by volume, a tolerance of 0.3 percent will be permitted, either above or below the stated percentage of alcohol. Any malt beverage which is labeled as containing 0.5 percent or more alcohol by volume may not contain less than 0.5 percent alcohol by volume, regardless of any tolerance.
In the EU,
- 0.5% vol. for beers having an alcoholic strength not exceeding 5.5 % vol. and beverages classified under subheading 22.07 B II of the Common Customs Tariff and made from grapes
- 1% vol. for beers having an alcoholic strength exceeding 5.5 % vol. and beverages classified under subheading 22.07 B I of the Common Customs Tariff and made from grapes; ciders, berries, fruit wines, and the like; beverages based on fermented honey
- 1.5 % vol. for beverages containing macerated fruit or parts of plants
- 0.3 % vol. for other beverages
There are two ways a brewery can measure the abv:
- By wort gravity: by measuring the specific gravity of the wort (the sugar solution that the yeast ferment into beer) both before and after fermentation. The difference is the amount of sugar consumed, which can be used to approximate the amount of alcohol produced.
- By distillation: the sample is heated, so the water and ethanol (alcohol) evaporate off and are collected in a condenser. The specific gravity of this is measured, which can then be used to calculate the percentage of alcohol, since the densities of alcohol and water are both known.
Both methods are exact and the accuracy is entirely due to the accuracy of the equipment used to measure.
The least accurate and precise is the case of (say) a microbrewer using a regular glass hydrometer to measure the OG and FG (method 1 above) - these read to 4 significant digits, with an accuracy of +/-1 SG at best. Without getting into the details, the accuracy then is about +/-5% of the final value for a regular strength beer. So for a 5% beer, that would be +/-0.25%.
With lab grade equipment, the accuracy of method 2 can be as good as 0.05%, since the specific gravities are measured with greater precision (and accuracy.) So our 5% beer would be with accuracy 0.0025%.