The O.G. was 13 Brix (1.053), and the F.G. was 8 Brix (1.031). According to the calculation, the beer is only approximately 3% ABV. But I tried a glass and it's gotta be closer to 5.5%. 20% of the grain bill was Crystal Malt 10L. Due to the residual unfermentable sugars from the crystal malt, is it possible that the alcohol content is actually much higher than my calculation suggests? If so, is there a more accurate way to calculate ABV?
How are you measuring gravity? I would double-check your gravity readings. If you are using a refractometer, you'll need to correct your reading because they are not meant to be used after fermentation begins (because of the presence of alcohol). If you're using a hydrometer, you need to de-gas your fermented sample enough to ensure that your hydrometer isn't being raised up due to the carbonation (I use a graduated cylinder as my hydrometer container, so I agitate my sample by putting my thumb over the top and shaking, and/or agitating the sample by moving my hydrometer up and down like a butter churn. Also, did you temperature-correct your readings?
If you're pretty confident in your gravity readings, how does it taste? From something that started and ended where yours did, I would expect it to taste pretty sweet and cloying. The calculation itself is pretty straight-forward and assumes that the difference in gravity is all due to sugar being converted to ethanol, so assuming your measurements are correct, I'm not sure how it could be that far off.
1.053 to 1.031 is only 41% apparent attenuation. I can't imagine that 20% crystal malt would produce enough unfermentable sugars for such low attenuation. Another source of unfermentatable sugars is a high mash temperature. Again, it would be difficult to get such a low attenuation from mash temperature number even if you were trying.
I think one of two things is going on.
Your yeast failed to ferment all the available sugars. To remedy this, pitch a new dose of fresh yeast.
Your final gravity reading was incorrect. As mentioned in other answers, using a refractometer and failing to adjust for the presence of ethanol is one possibility. Another is dissolved CO2 in the sample influencing the gravity reading.
I was using a refractometer and I failed to account for the EtOH in the solution. Using the link, I was able to calculate that the ABV was actually 4.3% rather than 3%. After I posted my original question, I had raised the temp to 62 degrees for a two day rest and then dropped it down to a lagering temp. I am proud to report that he final ABV is approximately 4.4%. I'm happy with this result and it means that my farm to table beer concept is actually working. You see, I grew everything from scratch. The barley. The hops. Malting the barley, drying the hops. Every step was done from scratch. I tasted the green beer and it will be good after lagering. Smooth. Nice mouth feel. Rich. But not too complex. Overall, a really good beer. I just hope it clarifies to perfection. I used PVPP (Polyclar) after fermentation. I dumped 3-4 pints out of the conical fermenter and I hope the rest drops out. I'm going to let it rest for a few more weeks and then transfer to a 5 gal keg and a 5 gal carboy. I want to see if more junk drops out in the carboy. For the keg, I'm curious to know if it drops out and then if it is able to be sucked out in the first few pints and then gets perfectly clear. Anyway, thanks guys for the help. I'm embarrassed to admit that I did not know that EtOH would screw up my F.G. readings. Love, from CA Becky the Brewer