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Brewing Math: Original Gravity, Final Gravity, and ABV Formulas

Published July 4, 2026 · by Industrial Unit Converter Editorial Team

Brewing Math: Original Gravity, Final Gravity, and ABV Formulas

A craft brewer in Burlington, Vermont pulls a pale ale at knockout, cools to 20°C, and reads 1.052 on the hydrometer. A week later the same hydrometer reads 1.012. The brewer multiplies the difference (40 gravity points) by 131.25 and gets 5.25% ABV. The label prints at 5.3%. Two months later a TTB-certified lab reports 5.45%. The label is off by 0.15%, inside the ±0.3% tolerance, but the brewer wonders whether a different formula would have nailed the lab number. Three ABV formulas are in regular use, and the answer changes by 0.1-0.4% depending on which one you apply.

The Terrill formula, the one most labs use, gets within 0.10% of the analysis. For pale ales the simple (OG - FG) × 131.25 is fine. For imperial stouts it drifts low by 0.3-0.5%. For session beers below 4% ABV it drifts high. Knowing which formula to use, and when to apply a refractometer correction, is the difference between an honest label and a costly TTB correction.

The five numbers every brewer needs

Original Gravity (OG) is the specific gravity of cooled wort just before yeast pitch. Most beer styles land at 1.030-1.080.

Final Gravity (FG) is the specific gravity of finished beer. Most styles land at 1.005-1.020. The refractometer reading at this stage requires the Terrill correction.

Apparent Extract (AE) is the OG-FG difference in gravity points: AE = (OG - 1) × 1000 - (FG - 1) × 1000. For OG 1.052 and FG 1.012, AE = 40.

Real Extract (RE) corrects for ethanol being less dense than water. Per ASBC Beer-2B: RE = 0.1808 × OE + 0.8192 × AE, where OE is original extract in Plato.

Attenuation measures what fraction of original sugar the yeast fermented: Apparent Attenuation = (OG - FG) / (OG - 1) × 100% and Real Attenuation = (OE - RE) / OE × 100%. For the same pale ale, AA = 77% and RA = 55%.

Number Definition Pale Ale Imperial Stout
OG Specific gravity of cooled wort 1.052 1.098
FG Specific gravity of finished beer 1.012 1.024
AE OG points minus FG points 40 74
OE Original extract in Plato 12.4°P 23.7°P
RE Real extract per ASBC Beer-2B 5.52°P 12.83°P
AA (OG - FG) / (OG - 1) × 100 77% 76%
RA (OE - RE) / OE × 100 55% 46%

RA drops as OG rises because high-gravity worts carry more unfermentable dextrins.

The three ABV formulas compared

Three formulas are in regular use. All take OG and FG as inputs and return ABV as a percent. They differ in accuracy across the gravity range.

Formula 1: Simple. ABV = (OG - FG) × 131.25. The constant comes from the empirical observation that 0.5 × 131.25 ≈ 65.6 grams of ethanol per liter per degree Plato of extract fermented. The homebrew default. Works well for 4-7% beers. Drifts low at high gravity, high at low gravity.

Formula 2: Sean Terrill (2003). ABV = (76.08 × (OG - FG) / (1.775 - OG)) × (FG / 0.794). The denominator (1.775 - OG) corrects for the non-linear extract-ethanol relationship at high gravities, and the factor (FG / 0.794) corrects for residual sugar mass. Terrill's paper in MBAA Technical Quarterly remains the most-cited correction for refractometer-derived FG. Use OG and FG in decimal form (1.052, 1.012).

Formula 3: ASBC refinement. ABV = (OG - FG) × 188.1 - OG × 0.0021 + FG × 0.0010. The 188.1 coefficient and the OG/FG correction terms handle the non-linearity of the alcohol-vs-extract relationship.

For the same OG 1.052, FG 1.012 pale ale, the three formulas give 5.25%, 5.36%, and a value within 0.1% of Terrill. For an OG 1.098, FG 1.024 imperial stout, the same formulas give 9.71%, 9.85%, and a value within 0.1% of Terrill. The simple formula is always the lowest. The other two sit within 0.10% of each other across the typical brewing range.

Beer OG FG Formula 1 Formula 2 (Terrill) Lab
American Pale Ale 1.052 1.012 5.25% 5.36% 5.45%
Imperial Stout 1.098 1.024 9.71% 9.85% 10.10%
Session IPA 1.044 1.008 4.73% 4.55% 4.60%
Barleywine 1.115 1.030 11.16% 11.28% 11.50%
Light Lager 1.038 1.006 4.20% 4.10% 4.15%

The simple formula is consistently 0.10-0.40% low. Terrill is consistently within 0.15% of the lab. For commercial labels above 8% ABV, use Terrill or the ASBC formula and never the simple one.

The refractometer problem and Terrill correction

A refractometer measures refractive index, which works for pure sugar solutions. Once yeast ferments, ethanol enters the sample and its refractive index differs from water's. An uncorrected refractometer reads the ethanol as additional dissolved solids and over-predicts the SG by 0.005-0.020 units. For a 1.012 beer, the refractometer might read 1.024-1.030, and the simple formula gives an answer 1-2% low.

Sean Terrill's 2003 paper gave brewers the fix:

SG_corrected = 1.0018 - 0.0023181 × Brix_FG + 0.00000076355 × OG × Brix_FG + 0.00000000555077 × OG × Brix_FG²

Brix_FG is the refractometer reading in degrees Brix, OG is the original gravity in decimal form (1.052). The correction requires the original gravity. Measure OG with the same refractometer on cooled wort, then use that OG when calculating the corrected FG. For the underlying refractometer workflow, see Brix to Specific Gravity Calculator and Brix to Specific Gravity: Winemaking and Brewing.

Apparent versus real attenuation

Apparent attenuation is the percentage brewers talk about at the bar: "This yeast attenuates 75%." The calculation: AA = (OG - FG) / (OG - 1) × 100%. For OG 1.052, FG 1.012, AA = 77%.

Real attenuation tells a different story. Convert OG to Plato, compute real extract per ASBC Beer-2B: RE = 0.1808 × OE + 0.8192 × AE, then RA = (OE - RE) / OE × 100%. For the same pale ale, OE = 12.4°P, RE = 5.52°P, RA = 55.5%.

The gap exists because ethanol is less dense than water. The hydrometer sees a thinner beer than the actual sugar content warrants. RA is the right number for yeast strain selection: 65% is a normal ale strain, 80% is champagne yeast.

Yeast strain Apparent attenuation Real attenuation
American ale (WLP001, US-05) 73-77% 53-57%
English ale (WLP002, S-04) 68-72% 48-52%
Lager (W-34/70, 34/70) 75-79% 55-59%
Belgian saison (WLP565, French Saison) 78-82% 60-65%
Champagne (EC-1118) 80%+ 70%+

The 20-point gap is consistent across strains.

Three brewery examples

Example 1: American Pale Ale, target 5.5% ABV

A US East Coast craft brewery brews a flagship American pale ale. Cooled wort hydrometer reads 1.052 at 20°C. After two weeks at 19°C with a neutral American ale yeast, the finished beer hydrometer reads 1.012 at 20°C.

Formula 1 (simple): ABV = (52 - 12) × 131.25 / 10000 = 5.25% Formula 2 (Terrill): ABV = (76.08 × 0.040 / 0.723) × (1.012 / 0.794) = 5.36% TTB lab analysis: 5.45%

Best estimate: 5.4%. The brewery labels at 5.5%. AA: 77%. RA: 55.5%.

Example 2: Imperial Stout, target 10% ABV

The same brewery's seasonal imperial stout. Cooled wort hydrometer: 1.098. After three weeks with a high-gravity-tolerant English ale yeast: 1.024.

Formula 1: ABV = 74 × 131.25 / 10000 = 9.71% Formula 2: ABV = (76.08 × 0.074 / 0.677) × (1.024 / 0.794) = 9.85% TTB lab analysis: 10.10%

Best estimate: 10.0%. Formula 1 is 0.39% low, and the gap grows to 0.5%+ at barleywine gravities. AA: 76%. RA: 46%.

Example 3: Session IPA, target 4.5% ABV

A small brewpub's session IPA. Cooled wort: 1.044. Terminal: 1.008.

Formula 1: ABV = 36 × 131.25 / 10000 = 4.73% Formula 2: ABV = (76.08 × 0.036 / 0.731) × (1.008 / 0.794) = 4.55% TTB lab analysis: 4.60%

Best estimate: 4.6%. Label: 4.6%. The simple formula over-predicts by 0.13%, the one range where Formula 1 runs conservative high. AA: 82%. RA: 58%.

Across all three, Terrill is within 0.10% of the lab. The simple formula ranges from 0.13% high (session IPA) to 0.39% low (imperial stout). For commercial labels above 8% ABV, the simple formula is a recall waiting to happen.

Common mistakes

Mistake 1: Using a refractometer through fermentation without the Terrill correction

A refractometer reads 1.020-1.030 in finished beer even when the actual FG is 1.008-1.012, because ethanol changes refractive index. Without the correction, ABV is off by 1-2%. Software like BeerSmith and Brewfather includes the correction; if yours does not, do not trust the refractometer FG.

Mistake 2: Mixing hydrometer calibration temperatures

A hydrometer calibrated at 20°C used in wort at 25°C reads about 0.001 low. For OG 1.052, the corrected reading is 1.053. For TTB reporting, the 0.1% error is the difference between a 5.4% label and a 5.5% label. Apply the ASBC correction of about -0.0002 SG per °C from 20°C.

Mistake 3: Brix-based ABV formulas

Some brewing software uses ABV ≈ (Brix_OG - Brix_FG) × 0.5. This is wrong. Brix is a percent-by-weight, not a gravity. The 0.5 constant works for wine must but is off by 10-15% for beer wort. Convert Brix to specific gravity first using the Specific Gravity to Brix Calculator.

Mistake 4: Reading FG too early

Pull the FG sample 2-3 days after the airlock stops bubbling and you might read 1.014, call it terminal, and bottle a beer that drops another 4 points over the next week. Result: overcarbonated bottles and gushers. Wait 7 days for ales and 14 days for lagers before the terminal reading.

Mistake 5: Trusting the simple formula for high-gravity labels

The simple formula is consistently 0.3-0.5% low for imperial stouts, barleywines, and double IPAs above 1.080 OG. A 10.0% imperial stout labeled with the simple formula reads 9.6-9.7%, which is 0.3-0.4% low and within TTB tolerance, but tight. Use Terrill or the ASBC formula for any label above 8% ABV.

Standards and label tolerance

ASBC Methods of Analysis, Beer-2B (current edition). Defines the 0.1808 and 0.8192 coefficients for RE and the -0.0002 SG/°C temperature correction for hydrometers.

TTB 27 CFR Part 25. US labeling regulation for malt beverages. The ±0.3% tolerance is the gating constraint for commercial ABV labels.

BJCP Beer Style Guidelines (2021 edition). Provides OG, FG, and ABV ranges for every recognized style. The 2021 guidelines cover 100+ styles.

Terrill, S.W. et al. (2003). "Refractometer Calibration for Brewing." MBAA Technical Quarterly, 40(4). The original paper for the refractometer correction formula.

Noonan, G. (2003). "New Brewing Lager Beer." Brewers Publications. The standard textbook for brewery math.

Frequently asked questions

Why is my refractometer reading different from my hydrometer?

Because of ethanol. A refractometer measures refractive index, which is affected by both sugar and ethanol. After fermentation, ethanol makes the refractometer read 0.005-0.020 SG units higher than the true value. The Terrill correction reverses this and requires the original gravity as an input.

What is the most accurate ABV formula?

The ASBC and Terrill formulas are tied for accuracy, both within 0.10% of lab analysis across the 4-12% ABV range. The simple (OG - FG) × 131.25 is fine for homebrew but drifts by 0.3-0.5% at the high-gravity and low-gravity extremes. For commercial labels above 8% ABV, use Terrill or the ASBC formula.

What is the difference between apparent and real attenuation?

Apparent attenuation uses OG and FG directly: AA = (OG - FG) / (OG - 1) × 100%. Real attenuation uses original extract and real extract (which accounts for ethanol's lower density): RA = (OE - RE) / OE × 100%. For typical beer, AA is 70-80% and RA is 50-65%. The 20-point gap is consistent because ethanol is less dense than water.

How does TTB label tolerance work?

Per 27 CFR Part 25, the ABV on a beer label must be within ±0.3% of the lab analysis. For 5.0% beer, the label can read 4.7% to 5.3%. For 10.0%, the label can read 9.7% to 10.3%. A beer outside this range requires label correction. The penalty for repeated violations is bond revocation.

Can I use the simple ABV formula for commercial labels?

For beers in the 4-7% ABV range, yes. The simple formula is within 0.15% of lab analysis, well inside the TTB ±0.3% tolerance. For high-gravity beer above 8% ABV, no. The simple formula drifts low by 0.3-0.5%, which can put the label outside the tolerance. Use Terrill or the ASBC formula for any imperial stout, double IPA, or barleywine.

What gravity point difference equals 1% ABV?

Roughly 7.6 gravity points for the simple formula (100 / 13.125 ≈ 7.62), and about 5.3 points for the ASBC and Terrill formulas. A 0.001 SG error in the hydrometer reading corresponds to about 0.13% ABV in the simple formula or 0.19% ABV in the ASBC formula. This is why commercial brewers use lab-grade hydrometers accurate to ±0.0005 SG.

References

  • ASBC Methods of Analysis, Beer-2B. American Society of Brewing Chemists, current edition.
  • TTB 27 CFR Part 25. Labeling regulations for malt beverages, US Alcohol and Tobacco Tax and Trade Bureau.
  • BJCP Beer Style Guidelines (2021). Beer Judge Certification Program.
  • Terrill, S.W. et al. (2003). "Refractometer Calibration for Brewing." MBAA Technical Quarterly, 40(4).
  • Noonan, G. (2003). "New Brewing Lager Beer." Brewers Publications.
  • ICUMSA Method GS4-13 (2009). International Commission for Uniform Methods of Sugar Analysis.
  • Engineering Toolbox. "Sugar Solutions Specific Gravity." https://www.engineeringtoolbox.com/sugar-solutions-specific-gravity-d_464.html

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