A pound of sugar per five gallons of beer will add nine points to the original gravity and reduce the final gravity by two points.
We’ve all heard it. I’m ashamed to say that I’ve even parroted it myself in the past. But it’s only half true.
The OG contribution of simple sugars is certainly easy enough to calculate. Most brewers are probably aware that potential extract is typically given as a percentage of the potential extract of pure sucrose (46.21 point-gal/lb, 96.39 °P-L/kg). Let’s assume a volume of 20 L (5.28 gal) just to make the math easy. For a 5.0-5.5 gal batch volume, that will get us within 5%, which I think most brewers would concede is “close enough”.
(96.39 °P-L/kg)(0.454 kg)/(20 L) = 2.19 °P = 1.00856
So if your batch volume is 5.5 gal, eight points might be a better rule of thumb, but the oft-quoted value is essentially correct.
Determining how sugars will affect the FG gets a little more complicated, because, let’s face it, for most of us it’s been a while since high school chemistry. There also has to be an assumption made about how much of the sugar is consumed, and how much is fermented. I think it’s reasonable to assume that a healthy, active population of yeast will consume nearly all of the simple sugars available. I’m going to further assume that the sugar is being added during the anaerobic fermentation phase, so that nearly all of it will be fermented, as opposed to being used for aerobic respiration. The amount of ethanol generated then becomes a simple question of stoichiometry. The relevant reaction is:
C12H22O11 + H2O → 4C2H5OH + 4CO2
So four moles of EtOH will be produced per mole of sucrose fermented. On a volumetric basis:
4((454 g)/(342.3 g/mol))(46.07 g/mol)/(0.789 g/mL) = 309.8 mL
Which is 1.525% ABV, incidentally. The reduction in density is a two-term weighted average:
(20000*1.0000 + 309.8*0.789)/(20000 + 309.8) = 0.9968
So when added to 20 L of water (or beer), a pound of fully-fermented sugar will actually reduce the SG by about 3.2 points, or 0.8°P. Maybe I’m splitting hairs here, but saying “two points” is off by about 60%.