According to an article from the Department of Food Science and Technology at UC Davis, the following forumula was provided:
The freezing point (°C) of beer = (-0.42 × A) + (0.04 × E) + 0.2, where A is the percent of alcohol content by weight, and E is the original gravity of the wort (°Plato). Therefore, each 1% increase in alcohol content lowers the freezing point by 0.42° C and each increase in gravity of 1° Plato raises it by 0.04°C. Thus, no beer will freeze at -1°C, and products at higher alcohol concentrations (including high-gravity brews prior to dilution) will withstand even lower temperatures.
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Yes, depending on the alcohol content, it will freeze anywhere between 32 degrees Fahrenheit (0 degrees Celsius) and -173 degrees Fahrenheit (-114 degrees Celsius). Beer, being relatively low in alcohol will freeze closer to 32 degrees as it is mostly water.
Since Wine freezes at about -7 degrees (Celsius) beer which has about half the alcohol of wine will freeze at about -3 to -4 degrees (Celsius) depending on the alcohol content of the beer.