Understanding the history of the labeling of alcoholic spirits can be more confounding than distilling the spirits themselves. A lot of this confusion stems from government regulations, which introduce another layer of historical perspective and complexity. For the modern imbiber of distilled spirits pondering the difference between proof and alcohol percentage by volume, it doesn't have to be so complex.
In the 1700s, if someone wanted to know that the whiskey they were purchasing was pure they had to "proof" it. This process entailed combining a small portion of the spirit with gunpowder and igniting it. If the liquid flamed up, it was proven; therefore, it had a certain proof. A steady burning blue flame meant it was a 100 proof spirit; a yellow flame that burned out quickly indicated an "overproof" spirit, meaning it contained more alcohol. If the mixture didn't burn,it was called "underproof," even though it may have contained alcohol.
The letters ABV in reference to an alcoholic beverage or the words "alcohol by volume" on a label simply refer to the percentage of alcohol the liquid contains. In the United States, if you double the percentage listed, you get the proof of the spirit, so, 40 percent alcohol would mean the liquor is 80 proof.
In the 18th century, a 40 percent alcohol by volume spirit would've been considered "underproof," but this term doesn't have much meaning anymore beyond a historical perspective. The majority of spirits sold these days, including many popular brands of whiskey, vodka and other liquors, are commonly between 80 to 90 proof. For spirits sold in the United States, listing a proof on the label isn't mandatory, although you will commonly see one printed alongside the required listing of the percentage of alcohol.
In the United States, proof is simply twice the percentage of alcohol, but that's not the case in other countries. Since original proofing methods weren't exact scientific measurements, they never were accurate for determining true alcohol content. Therefore, different scales of measurement were adopted over time. That's why, for instance, if you buy a bottle of cognac in the United Kingdom and then head to France to purchase the same-sized bottle of the same brand, it may be labeled differently.
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