How this calculator works
During fermentation, yeast turns sugar into ethanol and carbon dioxide. Each gram of sugar leaves less dissolved material, so the specific gravity of the liquid falls. The drop from original gravity to final gravity is therefore a proxy for the alcohol produced. The common approximation ABV = (OG - FG) x 131.25 is accurate enough for most beer, though the exact figure depends on the yeast and the wort composition. Alcohol by weight is lower than alcohol by volume because ethanol is less dense than water. US proof is twice the ABV; UK proof uses an older scale in which 100 proof is 57.15 per cent ABV.
Formula
ABV = (original gravity - final gravity) x 131.25, with gravity as a ratio above 1.000. Apparent attenuation = (OG - FG) / (OG - 1). ABW = ABV x 0.789 / final gravity. US proof = 2 x ABV. UK proof = ABV / 0.5715. Alcohol mass = serving volume x ABV x 0.789 kg/L, and energy = mass x 7 kcal/g.
Worked example
A beer falls from 1.050 to 1.010. The ABV is (1.050 - 1.010) x 131.25 = 5.25 per cent. The apparent attenuation is 0.040 / 0.050 = 80 per cent. ABW is 5.25 x 0.789 / 1.010 = 4.10 per cent. A 355 mL serving contains 355 x 0.0525 = 18.6 mL of pure alcohol, weighing 18.6 x 0.789 = 14.7 g, and providing about 103 kcal from alcohol alone.
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Frequently asked questions
Is the 131.25 factor exact?
No. It is a widely used approximation. More detailed formulas account for the density of the fermented beer and the proportion of sugar that becomes alcohol. For home brewing and label checking, the difference is usually within a few tenths of a percentage point.
Why is alcohol by weight lower than alcohol by volume?
Ethanol is lighter than water, 0.789 g/mL against about 1 g/mL. A liquid that is 5 per cent ethanol by volume therefore contains only about 4 per cent ethanol by weight. Labels in different countries use one or the other, so check which one is printed.
How is UK proof related to ABV?
The UK proof system dates from when spirit strength was tested by whether gunpowder would ignite. 100 degrees proof was set at 57.15 per cent ABV, so UK proof is roughly 1.75 times the ABV. The US uses a simpler scale where proof is exactly twice the ABV.
Does the calorie figure include the rest of the drink?
No, it is the energy from ethanol only. Residual sugars, proteins and other compounds add more, which is why the total energy on a beer label is higher than the alcohol figure shown here.