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From final gravity to the number on the label

Alcohol by volume
Applied to hydrometer readings only. Refractometers with ATC need no correction.
Need the label’s energy line? The calorie calculator takes it from here.
Alcohol by volume
7.0%
1.064 (15.7 °P) to 1.012 (3.1 °P)
Alcohol by weight
5.4%
Real extract
5.3°P
Apparent attenuation
80.4%
Real attenuation
65.9%
Calories per 33 cl
195
Calories per 12 oz
210

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ABV chart
Balling method. Rows are original gravity, columns final gravity. Tap a cell to load it into the calculator.
OGFG 1.005FG 1.010FG 1.015FG 1.020FG 1.025
1.040 (10.0 °P)4.64.03.32.62.0
1.045 (11.2 °P)5.34.64.03.32.7
1.050 (12.4 °P)6.05.34.74.03.3
1.055 (13.6 °P)6.76.05.34.74.0
1.060 (14.7 °P)7.36.76.05.34.7
1.065 (15.9 °P)8.07.46.76.05.4
1.070 (17.1 °P)8.78.07.46.76.0
1.075 (18.2 °P)9.48.78.17.46.7
1.080 (19.3 °P)10.19.48.88.17.4
1.085 (20.5 °P)10.810.19.58.88.1
1.090 (21.6 °P)11.510.810.29.58.8
1.095 (22.7 °P)12.211.510.910.29.5
1.100 (23.8 °P)12.912.211.610.910.2
Method

Alcohol is computed with the Balling method, with OE and AE the original and apparent extract in degrees Plato:

RE = 0.1808 × OE + 0.8192 × AE ABW = (OE − RE) / (2.0665 − 0.010665 × OE) ABV = ABW × FG / 0.7907

The quick formula, ABV = (OG − FG) × 131.25, is shown for comparison. Plato and SG conversions use the ASBC polynomial. Hydrometer readings taken away from calibration temperature are corrected with the standard water density polynomial, reading × f(T) / f(Tcal), with f(T) = 1.00130346 − 0.000134722124 × T + 0.00000204052596 × T² − 0.00000000232820948 × T³ and T in °F. Refractometer final readings are corrected with Terrill’s cubic formula, original and final Brix divided by the wort correction factor:

FG = 1 − 0.0044993 × OB + 0.011774 × FB + 0.00027581 × OB² − 0.0012717 × FB² − 0.0000072800 × OB³ + 0.000063293 × FB³

Calories use the usual estimate, [(6.9 × ABW) + 4.0 × (RE − 0.1)] × FG × 3.55 per 12 oz, scaled to 33 cl. Label tolerances: Regulation (EU) 1169/2011, Annex XII, kept as is in UK law; 27 CFR 7.65(c) in the US.

Questions

Why do two ABV calculators give different numbers?

The quick formula, (OG − FG) × 131.25, is a straight line fitted to average beers. Alcohol is lighter than water and the sugar left in the beer is heavier, so the line drifts as gravity rises. Balling’s method accounts for both. On a 1.050 beer finishing at 1.010 the gap is 0.07 percent; on a 1.090 beer finishing at 1.020 it is 0.3. Above 8 percent, use Balling.

What ABV can I print on the label?

In the EU and the UK, the stated figure may differ from the actual alcohol content by 0.5 percent vol for beers up to 5.5 percent, and by 1 percent vol above that (Regulation 1169/2011, Annex XII). In the US, the tolerance is 0.3 percentage points either way (27 CFR 7.65). Both apply to the alcohol content as measured, not as calculated from gravity.

Can I take the final gravity with a refractometer?

Yes, with a correction. Alcohol bends light more than the sugar it replaced, so a raw final reading is too high. Terrill’s cubic formula uses the original and final Brix readings, both divided by the wort correction factor, and returns a final gravity within hydrometer accuracy for typical beers. On very strong or very sweet beers, confirm with a hydrometer.

Formula and data: Sean Terrill, Refractometer FG results, 2011.

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