Hydrometer and refractometer corrections

Both instruments lie in ways you can correct for, and we correct for them the same way everyone else does, on purpose. A reading you check against another calculator should agree.

Hydrometers and temperature

A hydrometer is calibrated at one temperature, usually 60 °F, and reads low in a warm sample because the wort is less dense than the instrument assumes. The correction is the ratio of water’s density at the two temperatures. A sample at 30 °C reads about 1.6 points low.

Refractometers and wort

A refractometer is calibrated against sucrose, and wort is not sucrose. Its mix of maltose, dextrins and protein bends light more per unit of extract, so a raw reading runs about four percent high, and dividing by a wort correction factor takes that out. We default that factor to 1.04. If you have ever checked your refractometer against a hydrometer on the same unfermented sample, you can calibrate your own, which usually lands between 1.02 and 1.06.

Once fermentation has started

Once there is alcohol in the sample, a refractometer stops being a gravity instrument at all, because alcohol refracts far more strongly than sugar. The only way back is a model that knows where the wort started, and we use Terrill’s regression against measured hydrometer data. It is a fit, not physics. It stays sensible across the brewing range, and a widely circulated variant of it does not, which is why that variant is not here. The batch page switches to this correction on its own once the original gravity is in.

Volumes

We correct volumes too. A reading off a boiling kettle overstates the 20 °C volume by about four percent, and below 20 °C the correction runs the other way. The batch page’s volume fields take the hot reading and store the cold one.

The beer these numbers come from

Reference pale ale — 20 L into the fermenter, a 60 minute boil.

Grist	Amount	Color
Crisp Maris Otter Pale Ale Malt	4.5 kg	2.8 °L
Thomas Fawcett Caramalt	0.35 kg	9.9 °L

Hops	Amount	Alpha	Addition
Magnum	15 g	13.5 %	60 min boil
Cascade	30 g	6.8 %	10 min boil
Citra	40 g	13 %	20 min stand at 80 °C

It comes out at
Original gravity	1.0507
Final gravity	1.0094
Alcohol	5.52 %
Bitterness	35.66 IBU
Color	5.14 SRM (10.12 EBC)
Into the fermenter	20 L

The numbers

Gravity from a refractometer (unfermented wort)

1.0501 SG, from wort-correction-factor.

SG = SG(°P) where °P = Brix_measured / WCF
⇒ Gravity from a refractometer (unfermented wort) = 1.0501 SG

Input	Value	Unit
Measured brix	12.9	°Bx
Wort correction factor	1.04	—
Corrected brix	12.4	°Bx

What it assumes:

• A refractometer is calibrated against sucrose; wort refracts more per unit of extract, so a raw reading runs about 4 % high.
• Valid only before fermentation starts. Once there is alcohol in the sample, use the fermenting-sample model.

Sources:

• Methods of Analysis — American Society of Brewing Chemists

Final gravity from a refractometer

1.0084 SG, from terrill-linear.

FG = 1.001843 − 0.002318474·OB − 0.000007775·OB² − 0.000000034·OB³ + 0.00574·FB + 0.00003344·FB² + 0.000000086·FB³
⇒ Final gravity from a refractometer = 1.0084 SG

Input	Value	Unit
Original measured brix	12.9	°Bx
Final measured brix	6.4	°Bx
Wort correction factor	1.04	—
Corrected original brix	12.404	°Bx
Corrected final brix	6.154	°Bx

What it assumes:

• Alcohol refracts far more strongly than sugar, so a reading taken after fermentation started is meaningless without the starting point.
• OB and FB are wort-correction-factor-adjusted Brix, which is how Brewer’s Friend and Brewfather apply the same model.
• A widely circulated “Terrill cubic” variant returns gravities below 1.000 for strong beers and is deliberately not shipped.

Sources:

• Refractometer FG Results — Sean Terrill, 2011

Hydrometer reading corrected for temperature

1.0514 SG, from hydrometer-temperature-correction.

SG_true = SG_read × ρ(T_sample) / ρ(T_calibration)
⇒ Hydrometer reading corrected for temperature = 1.0514 SG

Input	Value	Unit
Measured gravity	1.048	SG
Sample temperature	30	°C
Hydrometer calibration temperature	15.56	°C
Correction points	3.42	gravity points

What it assumes:

• ρ is the cubic water-density fit in °F that every homebrewing calculator uses, so this agrees with the answer a brewer gets elsewhere.
• A hot sample reads low and the correction pushes it back up; a cold one reads high.

Sources:

• The homebrewing hydrometer temperature-correction polynomial (water density in °F)

Volume corrected to 20 °C

23.04 L, from kell-1975-density-ratio.

V_ref = V_t × ρ(t) / ρ(ref)
⇒ Volume corrected to 20 °C = 23.04 L

Input	Value	Unit
Volume	24	L
Measured at	100	°C
Expressed at	20	°C
Water density at the sample temperature	958.364	kg/m³
Water density at 20 °C	998.204	kg/m³
Shrinkage	3.991	%

What it assumes:

• Mass is conserved as the wort cools, so the volumes are in inverse ratio to the densities.
• Wort is treated as water. The error is smaller than the one significant figure the observed 4 % hot-wort shrinkage is quoted to.

Sources:

• Density, thermal expansivity, and compressibility of liquid water from 0° to 150 °C, J. Chem. Eng. Data 20(1), 97–105 — George S. Kell, 1975