What alcohol by volume actually measures, and why gravity can tell you
Alcohol by volume is the volume of pure ethanol in a beer divided by the volume of the beer, expressed as a percent. You never measure that directly at home. What you measure is density, twice: once before fermentation and once after. The difference between those two densities encodes how much sugar the yeast ate, and because the stoichiometry of alcoholic fermentation is fixed, the sugar consumed tells you the ethanol produced.
Yeast splits each molecule of fermentable sugar into roughly equal molar parts of ethanol and carbon dioxide. The carbon dioxide leaves through the airlock, so the beer loses mass. Ethanol stays, and ethanol is much lighter than water — about 0.789 g/cm3 against water's 0.998. Both effects push density down, which is why a finished beer reads lower than the wort it came from, and why a very well attenuated beer can finish below 1.000, lighter than plain water.
That double effect is also the source of every subtlety on this page. Your hydrometer cannot separate "sugar removed" from "alcohol added" — it only sees the combined density. The reading you get on finished beer is therefore called the apparent extract, and every simple ABV formula is a fitted correction that converts an apparent density drop into an alcohol figure. Once you know that, the difference between the two equations below stops being arbitrary.
Two readings, taken carefully, are all you need. Take the first from cooled wort just before you pitch, and take the second only after the gravity has held steady for three days — a beer still dropping is a beer whose ABV you cannot yet quote.
The two equations, and when each one is right
The everyday shortcut is ABV = (OG − FG) × 131.25. It says every thousandth of gravity you lose is worth about 0.13% alcohol. The factor is a straight-line fit through the real relationship, and over the gravity range most beer occupies — say 1.035 to 1.065 original gravity — it is accurate to about a tenth of a percent, which is finer than the precision of your hydrometer reading anyway. You will see 131, 131.25 and 132 all used; the spread between them is smaller than the error in reading a scale to the nearest half-point.
The extended equation, usually attributed to Michael Hall's 1995 Zymurgy treatment of gravity and alcohol, is ABV = 76.08 × (OG − FG) / (1.775 − OG) × (FG / 0.794). Read it in three pieces. The numerator 76.08 × (OG − FG) is the gravity drop scaled into alcohol by weight terms. Dividing by (1.775 − OG) is the correction that matters: as original gravity rises, the denominator shrinks, so the same gravity drop is credited with more alcohol. Multiplying by FG / 0.794 converts from a weight basis to a volume basis, since 0.794 approximates the specific gravity of ethanol and FG is the density of the beer the alcohol sits in.
At 1.070 original gravity and above, the extended equation always returns the larger of the two figures, and the gap grows with strength: a 1.092 wort finishing at 1.020 reads 9.45% by the shortcut and 10.30% by the extended equation, nearly a full point apart. That is why the automatic setting on this calculator switches over at 1.070. Below that the two agree closely enough that the choice is a matter of house convention.
Apparent attenuation is separate arithmetic and needs no fitting at all: (OG − FG) / (OG − 1.000). It is simply the fraction of the original gravity points that disappeared. Real attenuation corrects for the alcohol distortion by first estimating the real extract with the standard Balling relationship, RE = 0.1808 × OE + 0.8192 × AE, where OE and AE are the original and apparent extract in degrees Plato. Real attenuation always comes out lower than apparent attenuation for a beer that made any alcohol, typically by ten to fifteen points, because the ethanol was pretending to be missing sugar.
Calories follow from the same two numbers. The energy in beer is ethanol plus residual carbohydrate: kcal per 100 g = 6.9 × ABW + 4.0 × (RE − 0.1), the form given by George Fix. Multiply by the mass of your serving — millilitres times final gravity — and divide by a hundred.
Worked example: 1.060 down to 1.012
You brewed an American pale ale that started at 1.060 and finished at 1.012 after ten days. Serving size is a 12 fl oz bottle, which is 354.88 mL.
- Gravity drop. 1.060 − 1.012 = 0.048.
- ABV, simple equation. 0.048 × 131.25 = 6.30%.
- ABV, extended equation. 76.08 × 0.048 = 3.65184. Divide by (1.775 − 1.060) = 0.715 to get 5.10747. Multiply by 1.012 ÷ 0.794 = 1.274559 to get 6.51%. The beer is below 1.070, so the two answers sit two-tenths apart and either is defensible.
- Apparent attenuation. 0.048 ÷ 0.060 = 0.800, so 80.0%.
- Alcohol by weight. 6.30 × 0.789 ÷ 1.012 = 4.91%.
- Extract in Plato. Original: 259 − 259÷1.060 = 259 − 244.340 = 14.660 °P. Apparent: 259 − 259÷1.012 = 259 − 255.929 = 3.071 °P.
- Real extract. 0.1808 × 14.660 + 0.8192 × 3.071 = 2.651 + 2.516 = 5.166 °P.
- Real attenuation. (14.660 − 5.166) ÷ 14.660 = 64.8% — fifteen points below the apparent figure, exactly as expected.
- Calories. 6.9 × 4.91 + 4.0 × (5.166 − 0.1) = 33.89 + 20.27 = 54.16 kcal per 100 g. The serving weighs 354.88 × 1.012 = 359.14 g, so 54.16 × 3.5914 = 195 kcal.
Every step here is reproducible on paper. If the calculator disagrees with your arithmetic by more than a rounding step, the input is wrong, not the math.
How to read the result
Start with apparent attenuation, not with ABV. It is the number that tells you whether fermentation went the way you intended. Most ale strains land between 72% and 80% apparent attenuation on an all-malt wort mashed in the low 150s °F. English strains often stop around 68–72%; many Belgian and modern American strains push past 82%. A published attenuation range on a yeast pack is measured on a standard laboratory wort, so treat it as a guide to the strain's character rather than a promise about your recipe.
If your apparent attenuation lands well below the strain's range, the usual causes are, in order of frequency: an underpitch, a mash held too warm so that the wort was never that fermentable, and a fermentation that got cold and dropped the yeast out early. The yeast pitching rate calculator settles the first, and the strike water temperature calculator settles the second before you brew rather than after.
Attenuation well above the strain's range, on the other hand, points at something eating sugars your primary strain cannot: a diastatic Saccharomyces, Brettanomyces, or a wild yeast in the packaging line. A beer that keeps dropping months after packaging and gushes on opening is the classic signature, and it is a safety matter in glass.
ABV itself matters mainly for labelling, for competition categories and for tax. Style guidelines quote ABV ranges, and a beer entered one-tenth outside its range is judged as the style it claims to be, not the style it actually is. Since your reading precision is around ±0.1% at best, do not quote a batch to two decimals on a label you intend to defend.
Finally, use gravity as a fermentation-health check rather than only an accounting exercise. Two identical readings three days apart mean the beer is done. One reading means nothing at all — an airlock that has stopped bubbling is not evidence, since a slow leak in a bucket lid will stop bubbling long before the yeast stops working.
ABV from original and final gravity (simple equation)
| Original gravity | FG 1.006 | FG 1.010 | FG 1.014 | FG 1.018 |
|---|---|---|---|---|
| 1.040 | 4.46 | 3.94 | 3.41 | 2.89 |
| 1.050 | 5.78 | 5.25 | 4.73 | 4.20 |
| 1.060 | 7.09 | 6.56 | 6.04 | 5.51 |
| 1.070 | 8.40 | 7.88 | 7.35 | 6.83 |
| 1.080 | 9.71 | 9.19 | 8.66 | 8.14 |
| 1.090 | 11.03 | 10.50 | 9.98 | 9.45 |
| 1.100 | 12.34 | 11.81 | 11.29 | 10.76 |
From the 1.070 row down, the extended equation returns a higher figure than these — by about 0.4 points at 1.070 and about 0.9 points at 1.092. Use the table for quick orientation and the calculator, set to the extended equation, for anything you intend to print.
A refractometer lies about finished beer
Refractometers measure how much light bends passing through the sample, and ethanol bends light far more per unit mass than sugar does. On unfermented wort a refractometer is excellent and needs only the maker's wort correction factor. On fermented beer the raw Brix reading is high by several points, and feeding it into any equation on this page will overstate your final gravity and understate your ABV. Either take final gravity with a hydrometer, or apply a published refractometer correction — the widely used cubic fits from Sean Terrill and from Petr Novotný both take the original Brix, the final Brix and the wort correction factor — before you enter a number here.
Mistakes that put an ABV figure out by half a point
- Not correcting for temperature. A hydrometer is calibrated at one temperature, usually 60 °F or 20 °C. A sample read at 80 °F reads roughly 0.002 low. That is a quarter of a percent of alcohol on each end of the calculation.
- Taking original gravity from the kettle before the wort is mixed. Sugar and topping-up water stratify. Read from the fermenter after the wort is fully combined and stirred, or you are measuring one layer.
- Calling fermentation finished because the airlock stopped. Airlock activity measures pressure, not gravity. Two identical hydrometer readings three days apart is the only test that means anything.
- Using a refractometer for final gravity without correction. The single largest source of wrong ABV numbers in homebrewing.
- Forgetting sugar added after the original gravity reading. Dosing a Belgian dark strong with candi syrup on day three raises the alcohol without ever appearing in your OG. Add the sugar's gravity contribution to the original reading, or measure again after it dissolves.
- Ignoring priming sugar. Bottle conditioning adds roughly 0.2–0.3% ABV at normal priming rates. Work out how much you are adding with the priming sugar calculator if the number is going on a label.
Plato, Brix and where the laboratory methods differ
Specific gravity and degrees Plato measure the same thing on different scales. Plato states the extract as grams of sucrose per hundred grams of solution — a 12 °P wort has the same density as a 12% sucrose solution. Commercial brewers work almost entirely in Plato because it is a mass fraction and therefore adds and scales the way recipe arithmetic wants it to; homebrewers work in specific gravity because that is what cheap hydrometers are printed with. The conversion this page uses, °P = 259 − 259 / SG, is accurate to a couple of hundredths of a degree across the whole beer range.
Brix and Plato are separate scales built on sucrose solutions and are close enough to be treated as interchangeable at brewing concentrations; the difference is well under 0.1 °P below 20 °Brix.
Laboratories do not use any of this. The reference method in the ASBC Methods of Analysis distils the alcohol out of a weighed sample and measures the density of the distillate and of the residue separately, which gives real extract and alcohol independently rather than inferring one from the other. Modern breweries mostly use a benchtop density meter with a near-infrared or sonic alcohol channel that reproduces the distillation result in ninety seconds. Every equation on this page is a way of getting close to those numbers with a $10 glass tube, and it succeeds to about a tenth of a percent on ordinary beer.
Once you have a reliable ABV and attenuation figure, the rest of the recipe follows from other measurements taken the same day. The brewhouse efficiency calculator tells you whether your original gravity was the one the recipe intended, the IBU calculator gives you the bitterness-to-gravity ratio that decides whether the beer tastes balanced at that strength, and the keg carbonation calculator sets the pressure for serving it.
Key terms
- Original gravity (OG)
- The specific gravity of the wort immediately before yeast is pitched. Sets the ceiling on how much alcohol the batch can make.
- Final gravity (FG)
- The stable specific gravity of the finished beer. Called apparent final gravity because ethanol makes it read lower than the true dissolved solids would.
- Apparent attenuation
- The share of original gravity points that disappeared during fermentation. The number brewers quote and yeast labs publish.
- Real extract
- The dissolved solids actually left in the beer, with the ethanol effect removed. Drives body, sweetness and calories.
- Degrees Plato (°P)
- Extract expressed as grams of sucrose equivalent per hundred grams of solution. One degree Plato is about four gravity points at beer strengths.