The standard homebrew ABV equation is ABV = (OG, FG) x 131.25, where OG and FG are your original and final specific gravity readings. It is accurate up to about 6% ABV; above that, brewers switch to a more complex formula that corrects for the way sugar density stops behaving linearly at higher gravities.
The Standard Formula
ABV = (OG, FG) x 131.25
Original gravity (OG) measures the sugar content of your wort before fermentation starts. Final gravity (FG) measures what is left after the yeast finishes converting sugar into alcohol and carbon dioxide. The bigger the gap between the two readings, the more sugar got converted, and the stronger the beer. This version of the formula is old enough that its original source is hard to pin down exactly, though it is commonly attributed to a simplification of 19th-century work by Karl Balling, and it is the version used by Charlie Papazian in The Joy of Homebrewing, one of homebrewing’s most widely read references.
| Term | Meaning |
|---|---|
| OG | Original gravity, sugar density before fermentation |
| FG | Final gravity, sugar density after fermentation |
| 131.25 | A constant derived from ethanol’s density and the ratio of ethanol produced per unit of fermented sugar |
Why the Formula Works
During fermentation, yeast converts sugar into ethanol and CO2. Ethanol is lighter than water (specific gravity around 0.789), so as sugar gets replaced by alcohol, the overall density of the liquid drops. The gap between OG and FG is really measuring how much of that density drop happened, and the constant 131.25 converts that gravity drop into a percentage of alcohol by volume.
That constant itself breaks down into two smaller numbers: 1.05, which accounts for how many grams of ethanol are produced per gram of CO2 released (based on the molar masses of the two molecules), and a factor of roughly 0.80 for ethanol’s density relative to water, used to convert alcohol by weight into alcohol by volume.
The Advanced Formula, and When to Use It
The standard formula assumes a straight-line relationship between the gravity drop and the alcohol produced. That assumption holds up fine below roughly 1.070 original gravity (about 6-7% ABV), but above that point it starts underestimating the true alcohol content, by as much as a full percentage point once you get into barleywine or imperial stout territory. For those bigger beers, brewers use what is often called the Miller or Daniels formula:
ABV = (76.08 x (OG, FG) / (1.775, OG)) x (FG / 0.794)
| OG | FG | Standard ABV | Advanced ABV |
|---|---|---|---|
| 1.040 | 1.010 | 3.94% | 3.93% |
| 1.055 | 1.012 | 5.64% | 5.67% |
| 1.070 | 1.014 | 7.35% | 7.46% |
| 1.090 | 1.018 | 9.45% | 9.76% |
| 1.100 | 1.020 | 10.50% | 10.94% |
| 1.120 | 1.024 | 12.60% | 13.35% |
As the table shows, the two formulas agree closely below 1.070 OG, then diverge more and more as gravity climbs. For any beer above roughly 6% ABV, wine, mead, or cider made at home, the advanced formula is the one to trust for a label or a competition entry.
A Worked Example
Say you brewed an American IPA with an original gravity reading of 1.065 and a final gravity of 1.012. The standard formula gives: (1.065, 1.012) x 131.25 = 6.96% ABV. Run the same numbers through the advanced formula and you get 7.24% ABV, a meaningful 0.28 percentage point difference that matters if you are trying to label the beer accurately or enter it in a competition.
FAQ
What is the simplest way to calculate beer ABV?
Take an original gravity reading before fermentation and a final gravity reading after, then plug both into ABV = (OG, FG) x 131.25.
When should I use the advanced ABV formula instead of the standard one?
Once your original gravity goes above roughly 1.070, or your beer is likely to land above 6-7% ABV, the advanced (Miller or Daniels) formula gives a more accurate result.
Can I use a refractometer instead of a hydrometer for these formulas?
Yes, but you need a Brix-to-gravity conversion and a post-fermentation alcohol correction factor first, since alcohol changes how light bends through the sample in a way a hydrometer does not need to account for.
