A refractometer is one of the most useful tools a brewer can have. It allows for near-instantaneous measurements of specific gravity, without having to compensate for or adjust sample temperature or withdraw a large volume of wort/beer (a significant concern at homebrew scales). There are a few issues associated with accurately using a refractometer for brewing, though. First, a refractometer does not actually measure specific gravity, or sugar content. Instead it simply projects a line through a reticle, and relies on the fact that the refractive index of the fluid will move a line up and down the reticle. For a simple sucrose solution (the refractometers common to homebrewers are “borrowed” from the wine industry) the refractive index depends only on the sugar content and the temperature. Automatic temperature correcting (ATC) refractometers use a bimetal strip to cancel out the temperature variable (within a given range), meaning that the reticle can be marked directly in units of sugar content. Brewers’ wort, however, is not a sucrose solution, and so a “wort correction factor” must be applied. Generally this is done by dividing the refractometer reading by 1.04.
The second, more intractable problem with using a refractometer to determine specific gravity is that once fermentation begins, the beer becomes a three-part solution: sugars, water, and alcohol. There is no longer fidelity of measurement – that is to say, there can be more than one specific gravity that will correlate to the same refractive index. Generally speaking, however, only one of the potential data points will be sensible for a real beer. Making that assumption, it should be possible to develop a correlation between the measured refractive index and the actual gravity of the beer, as long as the alcohol content can be estimated. This means that if both pre- and post-fermentation readings are taken, the FG can be predicted. Various software packages and websites incorporate tools to do just that, all of which seem to use the same correlation:
FG = 1.001843 – 0.002318474*RIi – 0.000007775*RIi² – 0.000000034*RIi³ + 0.00574*RIf + 0.00003344*RIf² + 0.000000086*RIf³
Where RIi and RIf are the initial and final refractive indices, respectively, in wort-corrected degrees Brix.
I took pre- and post-fermentation readings of ten beers, with OGs ranging from 1.036 to 1.103, using both a refractometer and hydrometer. In every case the refractometer correlation provided an FG that was lower than the hydrometer reading, by anywhere from 0.5 to 8.5 “gravity points” (1000*(SG-1)). The mean discrepancy is 5.1 points. The main variable of concern seems to be the attenuation of the beer; the greater the attenuation, the larger the discrepancy. The results are plotted below.
Note that the discrepancy is zero at about 58% attenuation (71% apparent attenuation). I have no information on who originally developed the correlation, but my supposition is that they only tested worts with about this degree of fermentability. A logarithmic curvefit provides a reasonably good (R² ≅ 0.7) approximation for the offset that is needed; by adding this correction factor to the standard correlation, the maximum discrepancy for this dataset is reduced to only 2.1 points, and the average to 0.1 points. Unfortunately, the resulting equation is a bit unwieldy:
FG = (1.001843 – 0.002318474*RIi – 0.000007775*RIi² – 0.000000034*RIi³ + 0.00574*RIf + 0.00003344*RIf² + 0.000000086*RIf³) + 0.0216*LN(1 – (0.1808*(668.72*(1.000898 + 0.003859118*RIi + 0.00001370735*RIi² + 0.00000003742517*RIi³) – 463.37 – 205.347*(1.000898 + 0.003859118*RIi + 0.00001370735*RIi² + 0.00000003742517*RIi³)²) + 0.8192*(668.72*(1.001843 – 0.002318474*RIi – 0.000007775*RIi² – 0.000000034*RIi³ + 0.00574*RIf + 0.00003344*RIf² + 0.000000086*RIf³) – 463.37 – 205.347*(1.001843 – 0.002318474*RIi – 0.000007775*RIi² – 0.000000034*RIi³ + 0.00574*RIf + 0.00003344*RIf² + 0.000000086*RIf³)²))/(668.72*(1.000898 + 0.003859118*RIi + 0.00001370735*RIi² + 0.00000003742517*RIi³) – 463.37 – 205.347*(1.000898 + 0.003859118*RIi + 0.00001370735*RIi² + 0.00000003742517*RIi³)²)) + 0.0116
In order to spare anyone who might be interested some trouble, I’ve put together a simple spreadsheet that will calculate FG using both the old and new correlations, in addition to attenuation and ABV. If you end up using it for a significant number of batches, please share your results.
Update: 20 July 2010
I’ve since refined the FG correlation, using a more mathematically rigorous method. I leave the original post up for transparency’s sake, but if you’re looking for an FG calculator, please check out the new post.
Update: 07 Apr 2011