Refractometer and hydrometer

Refractometer: the wort correction factor

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 land between 1.02 and 1.06, and calibrating is worth doing:

WCF = Brix_measured / °P(hydrometer SG)

Take both readings on the same unfermented sample and the result is that instrument’s personal factor.

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.

Refractometer: a fermenting or finished sample

Alcohol refracts far more strongly than sugar, so a refractometer reading taken after fermentation has begun is meaningless without a correction that knows the starting point. Beerwright 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 hand the engine raw instrument readings instead and it will apply the factor to both for you.

It is called “linear” in the regression sense, not because the polynomial is first-order.

Original Brix	Final Brix	FG
12	6.5	1.0116
12	7	1.0147
16	9	1.0170

The model that was rejected

A second, widely circulated “Terrill cubic” was tried and not shipped. As transcribed it returns SG below 1.000 and implied attenuations above 100 % for strong beers, so its coefficients cannot be right.

The bar any replacement has to clear is written into the engine’s tests. Fed OB = FB — a sample that has not fermented at all — the shipped 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 %. Only one fermenting-sample model ships today; the parameter that selects it exists so a second can be added without a breaking change, not because a second exists.

Hydrometer: temperature correction

A hydrometer is calibrated at one temperature — 60 °F (15.56 °C) as standard — 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 deliberately not Kell’s equation, which the volume correction uses. Matching the other calculators is the point: check a reading against Brewer’s Friend and you should get the same answer here. The trade-off is that this fit is only good over the range a hydrometer sample is ever at, roughly 0–40 °C, and diverges badly outside it — fed 212 °F it returns 1.042, which is nonsense. That is exactly why the volume correction does not reuse it.