Refractometer Calculator: Brix to OG, FG and ABV

To read final gravity with a refractometer, divide both Brix readings by the wort correction factor, usually 1.04, then correct for alcohol with Sean Terrill's formula. Wort that read 13.0 °Bx and now reads 6.5 °Bx is at about 1.012, not the 1.025 the raw reading suggests: about 5.2% ABV.

How refractometer readings are corrected

A refractometer needs only a few drops of wort, so many brewers use it on brew day and during fermentation. Before fermentation, the reading converts directly to gravity. First divide it by the wort correction factor $k$ :

R = \frac{\text{°Bx}}{k}

The calculator then converts $R_i$ , the corrected original reading, to specific gravity with the same Brix conversion as Foambyte’s gravity converter.

Once fermentation starts, alcohol distorts the reading. Sean Terrill fitted two formulas to measured readings, both using the corrected original reading $R_i$ and the corrected current reading $R_f$ . The cubic one:

\begin{aligned} FG = {} & 1 - 0.0044993\,R_i + 0.011774\,R_f \\ & + 0.00027581\,R_i^2 - 0.0012717\,R_f^2 \\ & - 0.0000072800\,R_i^3 + 0.000063293\,R_f^3 \end{aligned}

and the linear one:

FG = 1 - 0.00085683\,R_i + 0.0034941\,R_f

ABV is then $(OG - FG) \times 131.25$ , and apparent attenuation is the share of the original gravity points that is gone.

For example, wort that read 13.0 °Bx before fermentation has an original gravity of 1.051. If the beer now reads 6.5 °Bx, the cubic formula gives a gravity of 1.012: about 5.2% ABV and 77% apparent attenuation. The uncorrected reading would suggest about 1.025.

Inside Foambyte, you record gravity readings for each batch in the unit you prefer and follow fermentation on the batch chart.

Reference table

Corrected gravity (SG) by original reading (rows) and current reading (columns) in °Bx, Terrill cubic formula with a wort correction factor of 1.04
Original \ current °Bx	4	5	6	7	8	9	10	12
10 °Bx	1.006	1.010	1.014	1.017	1.020	1.023	—	—
12 °Bx	1.004	1.008	1.011	1.015	1.018	1.021	1.026	—
14 °Bx	1.002	1.006	1.009	1.013	1.016	1.019	1.024	1.035
16 °Bx	1.000	1.004	1.007	1.010	1.014	1.017	1.021	1.033
18 °Bx	0.997	1.001	1.005	1.008	1.011	1.015	1.019	1.031
20 °Bx	0.994	0.998	1.001	1.005	1.008	1.011	1.016	1.027
22 °Bx	0.989	0.994	0.997	1.000	1.003	1.007	1.011	1.023
24 °Bx	0.984	0.988	0.991	0.995	0.998	1.001	1.005	1.017

Sources

Sean Terrill. “Refractometer FG Results”, seanterrill.com, 2011. Cubic and linear final gravity correlations and the 1.04 default wort correction factor.

Frequently asked questions

Why does a refractometer read wrong after fermentation starts?

A refractometer measures how much the sample bends light. Sugar and alcohol both bend light, but alcohol makes the sample lighter rather than denser, so once yeast turns sugar into alcohol the Brix reading no longer matches the gravity. The correction uses the original reading to estimate how much alcohol there is and removes its effect.

What is the wort correction factor?

Refractometers are calibrated for sugar dissolved in water, and wort contains other dissolved substances that bend light slightly differently. The wort correction factor divides each reading to account for that. Sean Terrill's correlations were fitted with 1.04, the usual default; you can measure your own by comparing refractometer and hydrometer readings of the same unfermented wort.

Should I use the cubic or the linear formula?

Both come from Sean Terrill's analysis of 68 sets of readings from several brewers. In his results the linear formula was slightly more accurate on average and the cubic slightly more precise. In his data, both were about as accurate as a typical homebrew hydrometer.

How accurate is a corrected refractometer reading?

For typical beers it is usually within a few gravity points of a hydrometer. Terrill notes that it fails for beers below about 50% real attenuation, such as some sweet stouts. To confirm a final gravity before packaging, measure it with a hydrometer.

Can I use this for cider or mead?

The correction was fitted to beer worts. Cider and mead musts have different sugars and often reach higher alcohol, so the results are less reliable there.