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How is alcohol strength in beer measured?

Most of the world measures alcohol as a percent of volume (abv).

In the U.S., alcohol in beer is measured by weight (abw). Since alcohol weighs roughly 20% less than water, abw measures appear 20% less than abv measures for the same amount of alcohol. In Europe, beer strength is mostly measured on the basis of the fermentables in the wort.

Until recently, Britain used OG, which is 1000 times the ratio of the wort gravity to that of water. Thus, a beer with an OG of 1040 was 4% more dense than water, the density resulting from dissolved sugars. You can generally take one tenth of the last two digits to estimate the percentage alcohol by volume once the dissolved sugars are fermented. In the example used, the abv would be approximately 4% (40/10 = 4%). Currently, British beer is being taxed on its actual %ABV rather than the older OG, hence it is common to find both criteria displayed.

Central Europe tends to use degrees Plato. In general, the degrees Plato are about one quarter of the last two digits of the OG figure. Thus, in our example above, the beer would be 10 degrees Plato. To get the expected alcohol by volume, divide the degrees Plato by 2.5.

Source : FAQ of alt.drinks.beer