Brewing ABV & Recipe Numbers, Explained

After reading this you can turn a pair of hydrometer or refractometer readings into alcohol by volume, attenuation and calories, size a corn-sugar priming charge for a target carbonation, and predict bitterness from a hop schedule using the Tinseth model.

What these numbers are and why they matter

A batch of beer starts as sugary wort and ends as a lighter, alcoholic liquid. The yeast eats sugar and produces roughly equal parts ethanol and carbon dioxide. Every brewing number you care about comes from measuring how far that conversion went.

Suppose you pitch yeast into wort with a specific gravity of 1.050, meaning it is 5.0% denser than water. Two weeks later the gravity has dropped to 1.010. That fall of 0.040 gravity points is the fuel the yeast burned. From it you can read out the alcohol content (about 5.3% ABV), how much of the sugar fermented (about 80%), and how many calories a can holds (about 153 per 355 mL). One measurement, several answers.

Gravity is the anchor. A hydrometer floats in the liquid and reads density directly. A refractometer reads how much the liquid bends light, in degrees Brix, which is fine before fermentation but needs correction afterward because alcohol bends light differently from sugar.

When to trust each measurement

Use a hydrometer when you can spare 100 mL or so of sample and the beer is near room temperature. It reads density with no assumptions about what is dissolved, so its final-gravity number is the honest one.

Use a refractometer when you want a fast reading from two drops, for example checking a boil or tracking a fermentation daily. Before fermentation it is accurate. After fermentation the raw Brix reading is far too high, and no simple linear fudge fixes it. The tool applies a wort-correction factor and the Terrill cubic to recover a usable final gravity.

An uncorrected refractometer final reading of 6.5 Brix looks like a gravity around 1.025, which would imply your beer barely fermented. The corrected value is closer to 1.008. Never compute ABV from a raw post-fermentation Brix number.

The formulas, and the intuition behind them

The quick ABV rule multiplies the gravity drop by a constant:

\text{ABV} \approx (\text{OG} - \text{FG}) \times 131.25

Here OG is original gravity and FG is final gravity. The constant 131.25 folds together the density of ethanol and the mass of sugar consumed per unit of gravity drop. It is a linear fit and it drifts high above about 7% ABV, because the relationship between gravity and alcohol is not truly linear.

The alternate formula corrects that curvature:

\text{ABV} = \frac{76.08 \cdot (\text{OG} - \text{FG})}{1.775 - \text{OG}} \cdot \frac{\text{FG}}{0.794}

The first fraction estimates alcohol by weight from the gravity change, scaled by how dense the starting wort was. The second factor, dividing final gravity by the density of ethanol (0.794), converts weight to volume. At 1.050 to 1.010 the two formulas agree within 0.1%. At a big 1.090 beer they can differ by half a percent ABV.

Attenuation tells you how much of the extract fermented. Apparent attenuation uses raw gravities:

\text{AA} = \frac{\text{OG} - \text{FG}}{\text{OG} - 1} \times 100\%

It is called apparent because dissolved alcohol is lighter than water, so it drags the final gravity below where the remaining sugar alone would put it. Real attenuation corrects for that and runs lower, roughly \text{RA} \approx 0.8192 \times \text{AA}.

Priming sugar and dissolved CO₂

Flat beer out of the fermenter still holds some carbon dioxide in solution. How much depends on the warmest temperature it reached: warmer beer holds less. Priming adds fresh sugar so a small secondary fermentation in the bottle produces exactly the extra CO₂ you want.

Residual CO₂ at temperature T in °C follows a fit close to:

\text{CO}_2^{\text{res}} \approx 3.0378 - 0.050062 \, T + 0.00026555 \, T^2

At 20 °C that gives about 0.86 volumes already dissolved. If your target is 2.4 volumes, you must generate the difference, about 1.54 volumes. Corn sugar (dextrose) yields roughly 4.0 g/L per volume of CO₂ added, so the charge is about 1.54 \times 4.0 \approx 6.2 g/L.

Bitterness with the Tinseth model

Hop bitterness comes from alpha acids that must be boiled to become soluble and bitter, a process called isomerization. Longer boils extract more, but denser wort extracts less. Glenn Tinseth captured both effects with a utilization factor:

U = \left(1.65 \cdot 0.000125^{\,\text{OG}-1}\right) \cdot \frac{1 - e^{-0.04 \, t}}{4.15}

The first bracket is the bigness factor: it shrinks as original gravity rises. The second is the boil-time factor, where t is minutes in the boil; it climbs steeply early and flattens after about an hour. IBU for one addition then combines utilization, the alpha-acid fraction, the weight and the batch volume:

\text{IBU} = \frac{U \cdot A \cdot m \cdot 1000}{V}

Here A is the alpha-acid fraction (6.5% is 0.065), m is grams of hops, V is litres, and the factor 1000 converts to mg/L, which is what an IBU approximates.

Utilization climbs fast in the first 20 minutes, then flattens. Doubling a boil from 60 to 120 minutes adds almost nothing.

A worked example with the demo data

OG 1.050, FG 1.010, 20 L, three hop additions

Load the demo data: hydrometer mode, OG 1.050, FG 1.010, 20 L batch, 2.4 volumes target, 20 °C, and three hop additions of 6.5%/30 g/60 min, 4.0%/20 g/15 min, 3.5%/15 g/5 min.

Quick ABV: (1.050 - 1.010) \times 131.25 = 5.25\%.
Alternate ABV: numerator 76.08 \times 0.040 = 3.043, divided by 1.775 - 1.050 = 0.725 gives 4.198% alcohol by weight, times 1.010 / 0.794 = 1.272 gives about 5.34% ABV.
Apparent attenuation: 0.040 / 0.050 = 80.0\%. Real attenuation: 0.8192 \times 80.0 = 65.5\%.
Calories per 355 mL come out near 153, most from residual carbohydrate, the rest from alcohol.
Priming: residual CO₂ at 20 °C is about 0.86 volumes, so add (2.4 - 0.86) \times 4.0 = 6.2 g/L, which is 123 g of corn sugar for 20 L.

Now the hops. Bigness factor at OG 1.050 is 1.65 \times 0.000125^{0.050} = 1.65 \times 0.6698 = 1.105.

Per-addition Tinseth contribution for the demo schedule (OG 1.050, 20 L)
Alpha %	Grams	Minutes	Utilization	IBU
6.5	30	60	0.2196	21.4
4.0	20	15	0.1089	4.35
3.5	15	5	0.0437	1.15

Total bitterness is about 26.9 IBU, dominated by the 60-minute charge. The late additions add aroma but little measured bitterness.

Reading and interpreting the results

Line the numbers up against style. An apparent attenuation of 80% is normal for a clean ale yeast: most brewing strains land between 72% and 82%. If yours reads 90%, suspect a wild yeast or bacterial infection eating sugars ordinary yeast leaves behind. If it reads 55%, the yeast stalled.

A bitterness-to-gravity check is the fastest sanity test on a recipe. Divide IBU by the last two OG digits: 26.9 / 50 = 0.54. Values near 0.5 read balanced, below 0.4 malty and sweet, above 0.8 sharply bitter.

The bittering charge does almost all the work. Late hops contribute flavor and aroma the IBU number does not capture.

Common mistakes

Temperature errors bite twice. A hydrometer is calibrated at a fixed temperature, often 20 °C, and reads low in warm samples. A reading of 1.008 taken at 30 °C actually corresponds to about 1.010 once corrected. Two gravity points shift your ABV by a quarter percent.

Always pull a hydrometer sample into a trial jar, cool it to the calibration temperature, and let bubbles clear before you read the meniscus. Bubbles clinging to the stem lift the float and fake a higher gravity.

The second frequent error is feeding the priming calculator the wrong temperature. Use the warmest point the beer reached, not the cold basement it now sits in. A beer that peaked at 22 °C holds less residual CO₂ than one kept at 12 °C, so it needs more priming sugar. Guess 12 °C when the truth was 22 °C and you under-carbonate by nearly half a volume.

Third, remember Tinseth IBU is a prediction, not a measurement. Hop age, pellet versus whole, vigor of the boil and how you dry hop all move real bitterness. Treat the number as a repeatable recipe target, not a lab value.

Related tools on this site

If your kitchen projects go beyond the fermenter, the Coffee Brew Ratio & Extraction Calculator applies the same measure-and-compute logic to coffee dose and yield. For baking, the Baker's Percentage & Dough Calculator scales a recipe from ratios to grams. And for precise low-temperature cooking, the Sous Vide Time & Safety Calculator handles come-up time and pasteurization holds.

Frequently asked questions

Why do the two ABV formulas disagree?

The ×131.25 rule is a straight line fit to a curved relationship. It matches the alternate formula closely below about 7% ABV and reads increasingly high above that. For the demo beer they differ by less than 0.1%, so either is fine; for a barleywine, trust the alternate formula.

Can I skip the refractometer correction?

No. Alcohol changes how the liquid bends light, so a raw post-fermentation Brix reading overstates the sugar left behind. The correction (a wort factor plus the Terrill cubic) is not optional if you want a believable final gravity.

How much does temperature change my priming sugar?

A lot. Residual CO₂ falls from about 1.1 volumes at 12 °C to about 0.86 at 20 °C to about 0.7 at 26 °C. At a 2.4-volume target that swings the corn-sugar charge from roughly 5.2 to 6.8 g/L, a 30% difference.

Why is real attenuation lower than apparent?

Ethanol is lighter than water, so it pulls the measured final gravity down, making the beer look more fermented than it is. Real attenuation strips out the alcohol effect. The factor 0.8192 is the standard conversion, so 80% apparent becomes about 65.5% real.

Does IBU tell me how bitter the beer tastes?

Only loosely. IBU measures isomerized alpha acids in mg/L, but perceived bitterness also depends on malt sweetness and body. Judge with the bitterness-to-gravity ratio: near 0.5 tastes balanced, above 0.8 tastes assertively bitter.

Try it yourself in the tool