Homebrew Numbers: ABV, Priming Sugar and Water Salts

Three calculations cover most of what a homebrewer needs to work out: how strong the beer is, how much sugar to add at bottling, and what to put in the water. The first is easy and slightly approximate, the second has a step everyone forgets, and the third is where people either overthink or ignore it entirely.

ABV from two gravity readings

Take a specific gravity reading before pitching yeast and another when fermentation is done. The difference is sugar that became alcohol.

Priming sugar, and the step everyone forgets

Bottle conditioning works by giving the remaining yeast a measured amount of sugar in a sealed bottle. The carbon dioxide they produce has nowhere to go, so it dissolves into the beer. Too little and the beer is flat; too much and you have bottle bombs, which is a genuine injury risk rather than a disappointment.

The step people miss is that the beer already contains dissolved carbon dioxide from fermentation, and how much depends on the temperature it has been sitting at. Warm beer holds less. So you do not prime for your target — you prime for the difference between your target and what is already in there.

Eighteen grams between a cool cellar and a warm room on the same batch. Use the highest temperature the beer has reached since fermentation finished, not the temperature right now — the dissolved CO₂ came out at the warmest point and did not go back in.

Water: two ions do most of the work

Brewing water chemistry has a reputation for complexity that mostly comes from people trying to replicate a historic city water profile. For a homebrewer the useful part is much smaller: two ions shape how the finished beer tastes, and the ratio between them is the lever.

• **Sulphate** accentuates hop bitterness and makes the finish drier and crisper. Gypsum (calcium sulphate) is how you add it.
• **Chloride** accentuates malt fullness and makes the beer taste rounder and sweeter. Calcium chloride is how you add it.
• **Calcium** matters for the mash rather than for flavour, and both of those salts bring it with them.

The same six grams, split differently, moves the beer from dry and bitter to soft and malty. That is the whole technique for most purposes: pick a direction, pick a ratio, and stop there. Chasing a Burton-on-Trent profile ion by ion is a much larger project with much smaller returns.

When the simple ABV formula drifts

The body of this guide warns that the 131.25 formula becomes an estimate above about 8%. It is worth seeing how large the drift is. Several online brewing calculators offer a second, more complex formula, generally attributed to an article by Michael L. Hall in Zymurgy in 1995. We could not obtain the original article to check it against, so treat it as a widely used alternative rather than a verified standard.

For a normal-strength beer the choice of formula makes no practical difference. For a barleywine or imperial stout it can change the answer by more than a percentage point, with the alternative reading higher. Neither is a laboratory measurement. If a precise figure matters, such as for a label, it has to come from a laboratory, not from gravity readings.

Gravity and degrees Plato

Recipes from professional brewers and from many countries quote sugar content in degrees Plato rather than specific gravity. Plato is the percentage of sugar by weight in the wort. A common approximation converts between the two.

Getting gravity readings you can trust

Every calculation in this guide is only as good as the two gravity readings behind it, and the readings have more ways to go wrong than the arithmetic does.

• **Correct for temperature.** A hydrometer is calibrated at a particular temperature, printed on it or in its instructions. Warmer liquid is less dense and reads low. Take the reading at the calibration temperature, or apply the correction the maker provides.
• **Read at the bottom of the curve.** Liquid climbs the hydrometer stem. Read where the flat surface of the liquid meets the scale, not the top of the curve.
• **Degas the sample.** Carbon dioxide bubbles cling to the hydrometer and push it up, reading high. Swirl or pour the sample back and forth first.
• **Confirm fermentation has finished.** Take two readings a few days apart. If they match, fermentation has stopped; if they differ, it has not, and bottling now risks over-carbonation.
• **Refractometers need a correction after fermentation starts.** Alcohol distorts their reading, so a refractometer's final gravity needs a correction formula before it is usable.

Priming sugar for any batch size

Priming sugar scales directly with volume. At a fixed target and conditioning temperature the dose per bottle is the same whatever the batch size, which gives a useful sanity check: for 2.4 volumes of carbon dioxide at 68°F it works out to about 2.2 grams of dextrose per 12-ounce bottle.

For a metric batch the arithmetic is the same: 20 litres at 20°C, which is 68°F, needs about 123 grams of dextrose for 2.4 volumes. Measure the batch you are actually bottling, after racking off the sediment, not the volume you started with. Several litres lost to trub and yeast is normal, and priming the original volume over-carbonates what is left.

What one gram of each salt adds

The water chemistry calculator works from the ion contributions of each brewing salt, derived from the salts' formula masses rather than copied from a chart. Here they are for one gram dissolved in 20 litres, a common homebrew batch size, so you can see the scale of each addition at a glance.

Scale by the grams you add and divide by your own batch volume. Two points are worth noting. Table salt adds sodium as well as chloride, so calcium chloride is usually the better way to raise chloride. And the figures for calcium chloride depend on which form you have, because it is sold in more than one hydration state. The calculator's figures, like its gypsum and Epsom salt figures, are for the hydrated forms (calcium chloride dihydrate, gypsum dihydrate, Epsom salt heptahydrate), so check your product's label.

Residual alkalinity: the number behind mash pH

The sulphate to chloride ratio decides flavour balance. The other number the calculator reports, residual alkalinity, decides something more fundamental: where the mash pH lands. The calculator uses Kolbach's formulation, which weighs the water's alkalinity against the calcium and magnesium that counteract it.

In the soft-water example earlier in this guide, residual alkalinity is about +8 before any additions, and adding gypsum or calcium chloride pushes it well below zero, to about −42 and −50 respectively. A low or negative residual alkalinity suits pale beers, because pale malts do little to lower the mash pH on their own. Dark roasted malts are acidic, so they tolerate, and can even need, more alkaline water; that pairing is the usual explanation given for why some historic dark-beer brewing centres had hard, alkaline water.

Common homebrew number mistakes

• **Reading a hydrometer at the wrong temperature.** Correct it, or cool the sample.
• **Bottling before fermentation has finished.** Two matching readings a few days apart, then bottle.
• **Priming the starting volume.** Prime the volume you are actually bottling.
• **Using the current temperature for priming.** Use the warmest the beer reached after fermentation.
• **Adding salts without a water report.** You are adding to what is already there, which may already be high.
• **Treating any ABV figure as exact.** Both formulas are estimates, and they diverge for strong beers.

Diluting hard water, worked through

If your tap water is hard and alkaline, adding salts cannot fix it, because salts only add ions. Dilution is the tool that takes them away. Mixing tap water with distilled or reverse-osmosis water reduces every ion in proportion, and the calculator shows the effect directly. Here is an illustrative hard water, not any particular city's supply, diluted in stages.

Two things happen at once as you dilute. Residual alkalinity falls, which is usually the goal, but calcium falls with it, and calcium matters for the mash and for yeast. That is why a common pattern is to dilute first and then add back calcium with a salt that also moves the flavour balance in the direction you want. On the 50% dilution above, adding 3 grams of calcium chloride to 20 litres lifts calcium back to about 96 ppm, drops residual alkalinity from about 70 to about 41, and swings the sulphate to chloride ratio from 1.33 to 0.32, towards a softer, maltier beer.

Gravity points: adjusting a recipe on brew day

Gravity readings can be treated as quantities of sugar, which makes brew-day adjustments simple arithmetic. Take the part after the decimal point as points, so 1.050 is 50 points, and multiply by the volume. The total stays the same when you add or remove water; only the concentration changes.

This is the arithmetic behind every correction on brew day. If your pre-boil gravity is low, you can boil longer to concentrate it, at the cost of a smaller batch, or add fermentable sugar or extract to add points. If it is high, you can top up with water, at the cost of a larger batch with the same total sugar. Knowing which lever you are pulling makes the decision quick.

When the final gravity comes out high

The body of this guide points out that apparent attenuation is the number that diagnoses a stalled fermentation. Once you know the attenuation is low, these are the usual causes to work through, roughly in order of how often they turn out to be the answer.

• **The fermentation is not actually finished.** Some yeasts slow down long before they stop. Take two readings a few days apart before concluding anything.
• **The fermentation temperature dropped.** Yeast slows sharply when it gets cold. Moving the fermenter somewhere a little warmer and gently rousing the yeast often restarts it.
• **Too little yeast was pitched,** or the yeast was old or stressed. An underpitched fermentation can stall well above the expected final gravity.
• **The mash was hotter than intended,** which produces more sugars the yeast cannot ferment. The beer will finish higher and fuller-bodied, and no amount of waiting fixes it.
• **The recipe has a lot of unfermentable content,** such as crystal malts, lactose or some extracts. A high final gravity may simply be what that recipe produces.
• **The yeast strain's normal range is lower than you assumed.** Check the manufacturer's stated attenuation range for the strain, and compare with that rather than with a general figure.

Only the first three are fixable after the fact. The last three are information for the next batch, which is exactly why recording original gravity, final gravity, mash temperature and fermentation temperature for every brew pays off: after a few batches the numbers tell you which of these is your usual problem.

Sources

• The ABV relation (OG − FG) × 131.25 and the apparent attenuation formula are the standard brewing approximations. The 131.25 is a fitted constant rather than a physical one, and the approximation drifts at high gravity.
• The residual CO₂ relation used for priming, 3.0378 − 0.05006 T + 0.0002655 T² with T in °F, is the standard brewing polynomial for dissolved carbon dioxide against temperature, as is the 15.113 g of dextrose per gallon per volume of CO₂.
• Ion contributions from each salt are computed from its formula mass using the IUPAC standard atomic weights: https://iupac.qmul.ac.uk/AtWt/

Where to go next

Ratios run through every kind of brewing. Coffee brew ratio explains why holding a ratio constant matters more than any other variable when batch size changes, and how to double or halve a recipe covers the same proportional reasoning in the kitchen, including the ingredients that refuse to take a multiplier.

Common questions