There are three main ways to measure liquid concentration in fractions:
molecular, and as a subcategory molar conentrations. Essentially, 5% of the molecules are alcohol, 95% water. Used primarily in chemistry and chemical engineering.
weight. The alcohol contributes 5% of the weight of the beer, the rest water.
volume. 5% of the 12 oz of beer is alcohol.
The same can of beer will give three different percentages of alcohol depending on which way you measure it.
Volume is the primary measurement of alcohol. Why that one was picked is beyond me. Like has been mentioned before, water and alcohol aren’t volumetrically additive. If you separate the 12 oz in a can of beer, you get two quantities of liquid that, if added mathematically, will equal more than 12 oz. It would seem mesuring it would be maddening.
But there was probably a historical concentration test that was in widespread use that happened to give the concentrations in volume, everyone used it, and it stuck.
Interestingly, in some states of the U.S., there are “3.2%” (pronounced “three two”) laws that have two tiers of beer (Kansas is one of them). Normal beer can be sold at liquor stores. Grocery and convienience stores can only sell 3.2% beer. Manufacturers have to make special blends that have a maximum of 3.2% alcohol. HOWEVER, the 3.2% is by weight instead of volume. So, the 3.2% is actually closer to 4.1% by normal (volume) measurments.
(Furthermore, Kansas law allows only beer and malt beverages to be sold at grocery and 7-11s, so wine cooler makers have to also make beer coolers (you have to check the fine print to see this), and they have to be under 3.2%alcohol by weight.)