Carbonation

Carbonation has two routes, and we treat them as the same question asked twice: how much CO₂ does the beer hold, and how do you get it to the target.

Forced carbonation

Force carbonating is a solubility problem. At a given temperature and a given pressure the beer holds a given volume of CO₂, and the fit behind that is the one every keg calculator uses. Ask for a target and a temperature and you get the regulator setting. It cannot overshoot, because the pressure is the target.

Priming

Priming is a mass balance. Your beer already holds some CO₂ from fermentation, the target says how much it should hold, and the difference is a mass of gas that a known mass of sugar makes. The yield per gram comes from the stoichiometry of fermentation and differs by sugar. Corn sugar is dextrose monohydrate, so the same carbon dioxide comes out of a heavier gram, and the dose runs about fifteen percent higher than table sugar.

The CO₂ already in the beer

The residual figure is read at the warmest temperature your beer reached at or after the end of fermentation, not the temperature it is at now. CO₂ that a warm diacetyl rest drove off does not come back when you crash the beer. The one exception is a schedule that finishes under pressure: a sealed vessel with a spunding valve on it really is at equilibrium, so that case is read from the pressure instead.

Why there is no keg rate

The folklore says to dose a keg below the bottle rate. The arithmetic does not support it: a corny keg’s headspace holds under four percent of the CO₂ the beer needs, and the one attributable source for the rule says it could not find where the rule came from. So a keg gets the bottle dose. If you want to be sure of not overshooting a keg, spund it, and the pressure is the target. The packaging page has the longer argument.

The beer these numbers come from

Reference pale ale — 20 L into the fermenter, a 60 minute boil.

Grist	Amount	Color
Crisp Maris Otter Pale Ale Malt	4.5 kg	2.8 °L
Thomas Fawcett Caramalt	0.35 kg	9.9 °L

Hops	Amount	Alpha	Addition
Magnum	15 g	13.5 %	60 min boil
Cascade	30 g	6.8 %	10 min boil
Citra	40 g	13 %	20 min stand at 80 °C

It comes out at
Original gravity	1.0507
Final gravity	1.0094
Alcohol	5.52 %
Bitterness	35.66 IBU
Color	5.14 SRM (10.12 EBC)
Into the fermenter	20 L

The numbers

Priming sugar

129 g, from priming-stoichiometric.

sugar_g = (target − residual) × beerVolume_L × 1.96 / CO₂ yield per gram of sugar
⇒ Priming sugar = 129 g

Input	Value	Unit
Beer volume	19	L
Target volumes	2.4	volumes CO₂
Fermentation temp	20	°C
Residual volumes	0.86	volumes CO₂
Volumes to add	1.54	volumes CO₂
CO₂ to generate	57.3	g
Sugar	corn-sugar	—
CO₂ yield of the sugar	0.4442	g CO₂ per g
Sugar per liter	6.79	g/L

What it assumes:

• Dosed as corn sugar (dextrose monohydrate), at 0.4442 g of CO₂ per gram.
• Residual CO₂ is read at the warmest temperature the beer reached at or after the end of fermentation, not the current one.
• A keg gets the same dose as a bottle. The folk reduction for kegs is not implemented, and the source that states it also disowns it.

Sources:

• Accurately Calculating Sugar Additions for Carbonation — Kai Troester (Braukaiser)
• CO₂ solubility in beer: the standard temperature and pressure carbonation tables
• Priming When Kegging — Brew Your Own, Mr. Wizard

Forced carbonation pressure

10.75 psi, from henry-law-carbonation-tables.

V = (P + 14.695) × (0.01821 + 0.09011 e^(−(T−32)/43.11)) − 0.003342, solved for P
⇒ Forced carbonation pressure = 10.75 psi

Input	Value	Unit
Temp	4	°C
Target volumes	2.4	volumes CO₂
Pressure	0.74	bar
Pressure	74	kPa
CO₂ in solution	4.7	g/L

What it assumes:

• PSI because that is how regulators are labeled; the same figure is given in bar and kPa above.
• Spunding to this pressure at the fermentation temperature reaches the target with no priming sugar at all.

Sources:

• CO₂ solubility in beer: the standard temperature and pressure carbonation tables
• Accurately Calculating Sugar Additions for Carbonation — Kai Troester (Braukaiser)