Where the formula comes from
Yeast turns sugar into alcohol and carbon dioxide. Sugar makes wort denser than water, alcohol makes it lighter, so the specific gravity falls from the original gravity (OG) before fermentation to the final gravity (FG) at packaging. The size of that drop tracks how much sugar became alcohol. The factor 131.25 converts the gravity drop into percent alcohol by volume for beers of normal strength. Some calculators use 131 or 132.7, which changes the result by a few hundredths of a percent.
The simple formula in Excel
Keep gravities as numbers such as 1.052, not as 1052 or "52 points". With OG in B2 and FG in C2, the formula is =(B2-C2)*131.25, which returns 4.2 for a light lager from 1.040 to 1.008. If you want a true percentage format, divide by 100: =(B2-C2)*131.25/100 formatted as %. For a quick mental check, every 0.001 of gravity drop (one "point") is worth about 0.13% ABV, so 40 points make about 5.25%.
The more accurate alternate formula
The simple factor assumes a typical beer. As the original gravity rises, the same gravity drop represents more alcohol, and the simple formula falls behind. The alternate formula used by many brewing calculators corrects for the gravity:
=(76.08*(B2-C2)/(1.775-B2))*(C2/0.794)
For the light lager both agree to within 0.01 points. For the amber ale the gap is 0.11 points, for the double IPA 0.56 and for the old ale 1.07 points. A rule of thumb from the table: below an OG of about 1.060 the simple formula is good enough. For strong beers, and whenever the number goes on a label, use the alternate formula or a laboratory measurement.
Worked example: ABV and attenuation of six beers
OG and FG are hydrometer readings (yellow). Both ABV formulas and the attenuation are filled down, the Plato block works through the amber ale.
| A | B | C | D | E | F | |
|---|---|---|---|---|---|---|
| 1 | Beer | OG | FG | ABV % (× 131.25) | ABV % (alternate) | Apparent attenuation |
| 2 | Light Lager | 1.040 | 1.008 | 4.20 | 4.21 | 80.0% |
| 3 | Amber Ale | 1.052 | 1.012 | 5.25 | 5.36 | 76.9% |
| 4 | Robust Porter | 1.058 | 1.015 | 5.64 | 5.83 | 74.1% |
| 5 | Double IPA | 1.080 | 1.014 | 8.66 | 9.23 | 82.5% |
| 6 | Belgian Tripel | 1.084 | 1.010 | 9.71 | 10.36 | 88.1% |
| 7 | Old Ale | 1.100 | 1.024 | 9.98 | 11.05 | 76.0% |
| 8 | ||||||
| 9 | Amber Ale in degrees Plato | Value | ||||
| 10 | Original extract (°P) ≈ 259 − 259 ÷ OG | 12.80 | ||||
| 11 | Apparent extract (°P) ≈ 259 − 259 ÷ FG | 3.07 | ||||
| 12 | Real extract (°P) = 0.1808 × OE + 0.8192 × AE | 4.83 | ||||
| 13 | Real attenuation | 62.3% | ||||
| 14 | Largest gap between the two ABV formulas (points) | 1.07 | ||||
- D3
=(B3-C3)*131.25Simple ABV - E3
=(76.08*(B3-C3)/(1.775-B3))*(C3/0.794)Alternate ABV - F3
=(B3-C3)/(B3-1)Apparent attenuation - F13
=(F10-F12)/F10Real attenuation - F14
=MAX(E2:E7-D2:D7)Largest gap between the formulas
Illustrative recipes. Both formulas are common homebrewing approximations, not laboratory methods. Check the local rules on home brewing and labelling, and if you drink, drink responsibly.
Apparent and real attenuation
Apparent attenuation is the share of the gravity points the yeast removed: =(B2-C2)/(B2-1). The amber ale reaches 76.9%, inside the typical 70–80% of many ale yeasts. It is called apparent because alcohol is lighter than water and makes the final gravity read lower than the sugar actually left.
The real attenuation corrects for that. Convert to degrees Plato (°P ≈ 259 − 259 ÷ SG): 12.80 °P original and 3.07 °P apparent extract. The real extract is 0.1808 × 12.80 + 0.8192 × 3.07 = 4.83 °P, so real attenuation is (12.80 − 4.83) ÷ 12.80 = 62.3%, roughly 0.82 times the apparent value.
From beer to spirits: proof and pure alcohol
Once you have ABV, related numbers follow directly. US proof is twice the ABV, so a 46% whisky is 92 proof. Litres of pure alcohol are volume × ABV, the basis of excise duty in many countries: 20 litres of a 5.25% beer contain 1.05 litres of pure alcohol. Spirits lose alcohol while they age in casks, which is covered in the angel's share calculation.
Common mistakes
- Typing gravity as points. 52 or 1052 instead of 1.052 makes the result 1,000 times too big or meaningless.
- Subtracting the wrong way. It is OG minus FG. FG minus OG gives a negative ABV.
- Using refractometer readings uncorrected. Alcohol distorts a refractometer's final reading, so FG from a refractometer needs a correction formula before it goes into the ABV formula.
- Skipping the temperature correction. Hydrometers are calibrated at one temperature, often 20 °C or 60 °F. A reading taken from warm wort is too low.
- Trusting the simple formula for strong beers. Above about 1.070 OG the 131.25 factor can understate ABV by half a point or more.
- Forgetting priming sugar. Bottle conditioning adds a little alcohol, roughly 0.1–0.3% depending on the sugar dose.
Frequently asked questions
What is the formula for ABV using OG and FG?
The simple formula is ABV % = (OG - FG) x 131.25. The more accurate alternate formula is ABV % = 76.08 x (OG - FG) / (1.775 - OG) x FG / 0.794, which matters mainly for strong beers.
How accurate is the 131.25 ABV formula?
For normal-strength beers it agrees with the alternate formula to within about 0.1 to 0.2 percentage points. For beers above about 1.070 original gravity it underestimates, by about 1 point for an old ale from 1.100 to 1.024.
Can I calculate ABV without an original gravity reading?
Not reliably with a hydrometer alone, because the formula needs the drop in gravity. You can estimate the OG from the recipe's malt and efficiency, or use a refractometer and hydrometer together with a correction formula.
What is apparent attenuation?
Apparent attenuation is (OG - FG) / (OG - 1), the share of gravity points the yeast removed. It is called apparent because alcohol lowers the final gravity reading. Real attenuation, which corrects for the alcohol, is roughly 0.82 times the apparent value.