The two formulas homebrewers use to turn gravity readings into alcohol by volume (ABV) agree to about a tenth of a percentage point at an original gravity of 1.050, and on our grid of 95 cases they part ways at 1.070. Original gravity (OG) is the wort's density relative to water before fermentation; final gravity (FG) is the same reading afterwards. From there the alternate formula read more than 0.3 points above the simple rule at every attenuation we tried, reaching 1.81 points at OG 1.120. The factor table published by HMRC, the UK tax authority, stayed within 0.37 points of the simple rule on either side, while the alternate read up to 1.47 points above it. None of these figures is a laboratory measurement.
Either homebrew formula swaps in for the other up to an original gravity of about 1.055
The simple rule is (OG − FG) × 131.25. The alternate, 76.08 × (OG − FG) ÷ (1.775 − OG) × FG ÷ 0.794, is attributed by brewing calculators to a 1995 Zymurgy article by Michael Hall, which we did not see. We ran both, plus two further estimates, for OG 1.030 to 1.120 in steps of 0.005, each at five levels of apparent attenuation between 60% and 90%. Attenuation is the share of the gravity above 1.000 that fermentation removed.
A point is a percentage point: 5.0% against 5.3% is a gap of 0.3 points. Up to OG 1.055 all four estimates stayed within 0.23 points of each other in all 30 cases. Above it they spread; these are our figures at 75% attenuation.
| OG / FG | Simple rule | Alternate | Balling model, curved scale | HMRC factor |
|---|---|---|---|---|
| 1.030 / 1.008 | 2.89% | 2.85% | 2.90% | 2.82% |
| 1.050 / 1.012 | 4.99% | 5.08% | 5.05% | 4.94% |
| 1.070 / 1.018 | 6.83% | 7.19% | 6.98% | 6.81% |
| 1.090 / 1.022 | 8.93% | 9.72% | 9.22% | 9.04% |
| 1.100 / 1.025 | 9.84% | 10.91% | 10.22% | 9.98% |
| 1.120 / 1.030 | 11.81% | 13.56% | 12.38% | 12.15% |
The formulas' gap crosses 0.3 points between OG 1.065 and 1.070. That is the whole tolerance 27 CFR 7.65(c) allows either side of the strength stated on a US malt beverage label, in force since 11 March 2022 under T.D. TTB-176; for most US beer the statement itself is optional. The UK's retained Regulation 1169/2011, Annex XII allows 0.5% vol for beer up to 5.5% and 1% vol above. Both bound a commercial label against a measured strength, a job no homebrew formula is meant to do, so here they serve only as scale.
The alternate formula replaces the sugar curve with a straight line
MEBAK, the German brewing-analysis commission, states Balling's relation in method B-590.10.070: "1 g of alcohol, 0.9565 g of carbon dioxide and 0.11 g of yeast are produced on average from 2.0665 g of extract." Extract is counted in degrees Plato, dissolved solids as a percentage by mass. Brewing calculators put the extract left in finished beer at 0.1808 of the original reading plus 0.8192 of the final one, a split absent from MEBAK's public abstract.
Our algebra: replace the curved conversion from gravity to Plato with the straight line °P ≈ 250 × (SG − 1), and the relation becomes 76.81 × (OG − FG) ÷ (1.7751 − OG) by weight, which FG ÷ 0.794 turns into volume. That is the alternate formula, except that its published 76.08 sits 0.95% below 76.81. We cannot say this is how it was derived. It does make the alternate and the curved-scale column one model on two sugar scales, so that column is no independent check. The straight line reads Plato higher as gravity rises: 25.0 °P at SG 1.100, against 23.77 on the calculator's cubic gravity-to-Plato curve. At OG 1.100 and FG 1.025, changing the extract split, the Plato conversion or the density of ethanol kept our curved-scale figure between 10.08% and 10.35%, at least 0.56 points under the alternate.
Until 12 October 2026 the calculator on our beer ABV page told readers in seven places to read the alternate for strong beer, ranking it above the simple rule with no source. It also promised Brix formulas it lacked and printed −2,951.21% for an OG of 1.8 and an FG of 1.1. The revision of that date shows both at equal weight beside HMRC's factor, and refuses an OG above 1.200 or an FG below 0.990.
A sliding factor stands in for 131.25 in HMRC's duty guidance
Section 11.8 of HMRC's Alcoholic products technical guide lets brewers "with no or minimal laboratory facilities" multiply the drop in gravity by a factor, f. Gravity is in UK degrees, so 1.040 is written 1040. The factor, from a table by the Laboratory of the Government Chemist, rises across eleven bands from 0.125 for the smallest drops to 0.135 for the largest. HMRC's reason: "in lower strength beer, more of the ‘sugars’ available for fermentation are consumed in yeast reproduction than in producing alcohol." It puts most popular UK beers at 0.129 to 0.130.
In those units 131.25 is a fixed factor of 0.13125, between the table's 0.131 and 0.132 bands. On a 5% beer it reads 0.05 to 0.09 points higher than HMRC's factors for popular beers, by our arithmetic. We could not trace 131.25 to any source we could open.
Singapore's duty sum trades litres of beer for litres of alcohol
Singapore Customs' list of dutiable goods, last updated on 9 March 2026, says duty on intoxicating liquors "may be based on" litres of alcohol: quantity in litres × duty rate × percentage of alcoholic strength. Because strength multiplies the whole sum, a 5% beer stated at 5.5% changes the duty by a tenth, on our arithmetic.
For UK duty, HMRC measures ABV at 20°C and rounds it down to one decimal place. In Malaysia, the Food (Amendment) (No. 3) Regulations 2025 (P.U. (A) 345/2025), gazetted on 30 September 2025 and in force from 1 April 2026, replaces "2 per cent" with "0.5 per cent" in regulation 361(1) of the Food Regulations 1985. Regulation 361 is the general standard for alcoholic beverages, so the change moves the strength at which a drink falls under it. It is not a rule on declaring ABV or on label tolerance.
Refractometers substitute refraction for density, which alcohol skews
Every formula above takes density, which a floating hydrometer reads. A refractometer reads how far a few drops bend light. MEBAK's refractometric method states that refraction "is a function of concentration (alcohol/extract), temperature and wavelength", and derives alcohol and original gravity from the refractive index together with density. After fermentation alcohol sits beside the extract, and a refractive reading alone cannot say how much of the bend each causes.
Distillation takes the place of every gravity formula in the UK's legal method
Schedule 2 of the Alcoholic Products (Excise Duty) Regulations 2023, reproduced in section 11.7 of HMRC's guide, fixes the strength of beer by laboratory analysis. A measured sample, cleared of sediment and gas, is distilled and made back up to volume with distilled water at 20°C; the distillate's density, found with a pycnometer, a flask of exactly known volume, is read against the Laboratory Alcohol Table. In a dispute HMRC officers take samples, and the analysis "will establish the actual dutiable strength of the product". Beside it, the section 11.8 factor method is a shortcut, and HMRC says of its own table that it "is primarily for your guidance".
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