The wort correction factor, reading a fermenting sample with a refractometer, and correcting a hydrometer reading for temperature.
A refractometer is calibrated against sucrose, but wort's mix of maltose, dextrins and protein refracts more per unit of extract, so a raw reading runs high by about 4 %:
Brix_corrected = Brix_measured / WCF
The default WCF is 1.04. Brewers who calibrate their own instrument against a hydrometer typically get between 1.02 and 1.06, so it's worth calibrating yours:
WCF = Brix_measured / °P(hydrometer SG)
Take both readings on the same unfermented sample, and the result is the factor for that instrument.
With the default factor, a 12 °Bx reading corrects to 11.54 °Bx, which is SG 1.0464.
This is only valid before fermentation starts.
Alcohol refracts far more strongly than sugar, so a refractometer reading taken after fermentation has started is meaningless unless the correction also knows the original reading. The engine uses Sean Terrill's linear regression against measured hydrometer data ("Refractometer FG Results", seanterrill.com):
FG = 1.001843 − 0.002318474·OB − 0.000007775·OB² − 0.000000034·OB³
+ 0.00574·FB + 0.00003344·FB² + 0.000000086·FB³
OB and FB are the corrected Brix readings (original and final, both
divided by the WCF), which is how Brewer's Friend and Brewfather apply the same
model. You can pass raw instrument readings instead, and the factor is applied
to both.
It's called "linear" in the regression sense. The polynomial isn't first-order.
| Original Brix | Final Brix | FG |
|---|---|---|
| 12 | 6.5 | 1.0116 |
| 12 | 7 | 1.0147 |
| 16 | 9 | 1.0170 |
We tried a second, widely circulated "Terrill cubic" and didn't use it. As transcribed it returns SG below 1.000 and implied attenuations above 100 % for strong beers, so its coefficients can't be right.
The tests set the standard any replacement has to meet. Given OB = FB (a
sample that hasn't fermented at all), the current model returns within 0.002 SG
of the true gravity of that Brix from 8 to 20 °Bx, and over realistic
fermentations it implies apparent attenuations of 69–75 %. There's only one
fermenting-sample model. The parameter that selects it is there so a second can
be added later without a breaking change.
A hydrometer is calibrated at one temperature, usually 60 °F (15.56 °C), and a sample at any other temperature reads wrong:
SG_true = SG_read × ρ(T_sample) / ρ(T_calibration)
Hot samples read low, because the wort is less dense than the instrument assumes, and the correction pushes them back up. A 30 °C sample read as 1.050 is really 1.0534. Cold samples correct the other way, and the size of the correction grows with the gap.
The density here uses the cubic fit against °F that every hydrometer-correction calculator in homebrewing uses:
ρ = 1.00130346 − 1.34722124e-4·T + 2.04052596e-6·T² − 2.32820948e-9·T³
This is not Kell's equation, which the volume correction uses. We use this fit to match the other calculators, so a reading checked against Brewer's Friend gives the same answer. The downside is that it's only good over the range a hydrometer sample is realistically at, roughly 0–40 °C, and is badly wrong outside it (at 212 °F it returns 1.042). That's why the volume correction doesn't use it.