Zusammenfassung
ABV (Alcohol By Volume) calculators convert Stammwürzewerte into alcohol percentage. The Standard formula (ABV = (OG − FG) × 131.25) works well for beers under 6% ABV, while the Miller formula provides better accuracy for high-gravity brews above 8%. When using a refractometer, you must apply a Brix-to-gravity conversion and a post-Gärung correction factor because alcohol changes the refractive index of your sample. Dieser Leitfaden führt durch every formula, compares their accuracy ranges, and provides worked examples for beer, wine, mead, and cider.
Why ABV Matters Beyond Bragging Rights
Knowing your alcohol content is not just about labelling your bottles at the next homebrew competition. ABV directly affects:
- Flavour perception: Alcohol contributes body, warmth, and can mask or amplify hop Bittere and residual sweetness.
- Yeast health: A stuck Gärung at 1.030 versus a clean finish at 1.010 tells you very different stories about your yeast’s performance.
- Legal compliance: In many jurisdictions, Hobbybrauer face volume limits and commercial brewers must declare ABV within tight tolerances (typically ±0.5%).
- Recipe iteration: Tracking ABV across batches helps you dial in efficiency and Vergärungsgrad.
Die gute Nachricht ist that a reliable ABV calculation only requires two Stammwürzewerte and the right formula.
ABV CalculatorCalculate your alcohol by volume from Stammwürzewerte
Understanding Gravity: The Foundation of ABV Calculation
What Is Spezifische Dichte?
Specific gravity (SG) is the density of your Würze or must compared to pure water. Water has an SG of 1.000 at 15.6 °C (60 °F). Dissolving fermentable sugars raises that number — a typical pale ale Würze might read 1.050, meaning it is 5% denser than water.
During Gärung, yeast converts sugar into ethanol and CO₂. Ethanol is less dense than water (SG ≈ 0.789), so the gravity drops. The difference between your Stammwürze (OG) and Restextrakt (FG) tells you how much sugar was consumed, from which we infer alcohol production.
Gravity Skalas at a Glance
| Skala | Einheit | Beziehung zu SG | Verbreitung |
|---|---|---|---|
| Spezifische Dichte (SG) | Dimensionless ratio | Baseline | Beer, cider |
| Degrees Plato (°P) | Grams of sucrose per 100 g solution | °P ≈ (SG − 1) × 1000 / 4 | Professional brewing |
| Degrees Brix (°Bx) | Grams of sucrose per 100 g solution | Nearly identical to Plato for Würze | Wine, mead, refractometers |
| Gravity Einheits (GU) | Points | GU = (SG − 1) × 1000 | Homebrew shorthand |
For practical purposes, Plato and Brix are interchangeable in pre-Gärung Würze. Their readings diverge slightly post-Gärung because the Brix scale was calibrated for sucrose solutions, not ethanol-sugar mixtures. This is exactly why Refractometer Post Gärung Correction is essential when using a refractometer.
The Standard ABV Formula
The most widely used formula in Hobbybrauen is:
ABV = (OG − FG) × 131.25
This equation is sometimes attributed to the simplification of the more complete work by Balling in the 19th century. It assumes a linear relationship between gravity drop and alcohol production.
Worked Example: American Pale Ale
| Parameter | Wert |
|---|---|
| OG | 1.052 |
| FG | 1.012 |
| Gravity drop | 0.040 |
| ABV | 0.040 × 131.25 = 5.25% |
This is clean, simple, and accurate enough for the vast majority of session-strength beers.
Where the Standard Formula Falls Short
The linear approximation breaks down at higher gravities because the relationship between sugar concentration and density is not perfectly linear. Above approximately 1.070 OG (or about 6–7% ABV), the standard formula begins to underestimate true ABV by an increasing margin. By the time you reach a 1.100 barleywine, the error can be 0.5–1.0% ABV.
The Miller Formula (Alternate ABV Calculation)
Dr. David Miller proposed an alternative formula that uses a polynomial correction:
ABV = (76.08 × (OG − FG) / (1.775 − OG)) × (FG / 0.794)
This formula accounts for the non-linear density changes at higher sugar concentrations and the density of ethanol more precisely.
Comparison: Standard vs Miller
| OG | FG | Standard ABV | Miller ABV | Lab ABV (reference) |
|---|---|---|---|---|
| 1.040 | 1.010 | 3.94% | 3.93% | 3.95% |
| 1.055 | 1.012 | 5.64% | 5.67% | 5.68% |
| 1.070 | 1.014 | 7.35% | 7.46% | 7.50% |
| 1.090 | 1.018 | 9.45% | 9.76% | 9.82% |
| 1.100 | 1.020 | 10.50% | 10.94% | 11.02% |
| 1.120 | 1.024 | 12.60% | 13.35% | 13.48% |
Wie du sehen kannst, the divergence becomes meaningful above 1.070. For a Belgian tripel, imperial stout, or any wine or mead, the Miller formula is the better choice.
Which Formula Should You Use?
| Scenario | Empfohlene Formel |
|---|---|
| Session beers (< 5% ABV) | Standard — simple, accurate enough |
| Mid-range beers (5–7% ABV) | Either — difference is < 0.2% |
| High-gravity beers (> 7% ABV) | Miller — meaningfully more accurate |
| Wine (10–15% ABV) | Miller or dedicated wine formula |
| Mead (8–18% ABV) | Miller — essential for accuracy |
| Cider (4–8% ABV) | Standard for dry cider, Miller for ice cider |
Working with Brix and Refractometers
A refractometer measures the refractive index of a liquid and reports it in degrees Brix. Pre-Gärung, the conversion from Brix to SG is straightforward:
SG = 1 + (Brix / (258.6 − (Brix × 227.1 / 258.2)))
Or the simplified version many calculators use:
SG ≈ 1.000019 + (0.003865613 × Brix) + (0.00001318441 × Brix²) + (0.00000006922 × Brix³)
The Post-Gärung Problem
After Gärung begins, alcohol in the sample changes the refractive index. A refractometer will read higher than the actual gravity because ethanol bends light differently than a sugar-water solution. A reading of 8 °Brix on your refractometer might correspond to an actual FG of only 1.010 rather than the 1.032 the Brix reading would suggest.
This is why you must apply a correction — see our detailed guide on Refractometer Post Gärung Correction for the Terrill linear and cubic formulas, correction tables, and Schritt für Schritt instructions.
Wort Correction Factor (WCF)
Brewing Würze is not a pure sucrose solution. It contains maltose, maltotriose, dextrins, proteins, and other compounds that affect the refractive index differently. The Wort Correction Factor (typically 1.02–1.06, with 1.04 as the standard default) compensates for this:
Corrected Brix = Measured Brix / WCF
If your refractometer consistently reads slightly high compared to your hydrometer, calibrate your personal WCF by taking parallel readings on the same sample.
Praktische Beispiele für verschiedene Getränkearten
Example 1: English Bitter (Beer)
| Parameter | Wert |
|---|---|
| OG (hydrometer) | 1.038 |
| FG (hydrometer) | 1.008 |
| Standard ABV | (0.030) × 131.25 = 3.94% |
| Miller ABV | 3.92% |
| Apparent Vergärungsgrad | 78.9% |
For a session bitter, both formulas agree. The standard formula is perfectly adequate.
Example 2: Belgian Tripel (Beer)
| Parameter | Wert |
|---|---|
| OG (hydrometer) | 1.082 |
| FG (hydrometer) | 1.010 |
| Standard ABV | (0.072) × 131.25 = 9.45% |
| Miller ABV | 9.72% |
| Apparent Vergärungsgrad | 87.8% |
The 0.27% difference matters for a competition entry or commercial label. Use Miller here.
Example 3: Semi-Sweet Mead
| Parameter | Wert |
|---|---|
| OG (refractometer, corrected) | 1.120 (28.1 °Bx) |
| FG (hydrometer, post-ferment) | 1.022 |
| Standard ABV | (0.098) × 131.25 = 12.86% |
| Miller ABV | 13.23% |
| True ABV (lab estimate) | ~13.4% |
For mead, the Miller formula gets you within 0.2% of laboratory results, while the standard formula undershoots by over 0.5%.
Example 4: Dry Cider
| Parameter | Wert |
|---|---|
| OG (hydrometer) | 1.055 |
| FG (hydrometer) | 1.002 |
| Standard ABV | (0.053) × 131.25 = 6.96% |
| Miller ABV | 7.08% |
| Apparent Vergärungsgrad | 96.4% |
Cider often ferments very dry. The standard formula is acceptable for most ciders, but if you are working with high-sugar heritage apple juice (OG > 1.070), switch to Miller.
Example 5: Off-Dry White Wine
| Parameter | Wert |
|---|---|
| OG (refractometer) | 1.090 (21.5 °Bx) |
| FG (hydrometer) | 1.006 |
| Standard ABV | (0.084) × 131.25 = 11.03% |
| Miller ABV | 11.38% |
Wine typically demands the Miller formula. Most winemaking software uses it or a variant by default.
Häufige Fehler und wie du sie vermeidest
1. Ignoring Temperature Correction
Your hydrometer is calibrated at a specific temperature — usually 15.6 °C (60 °F) or 20 °C (68 °F). Taking a reading at 30 °C (86 °F) straight from the Gärbehälter introduces a significant error. Our Gravity Temperature Correction Guide explains the correction formula and provides tables so you never have to guess.
2. Reading the Meniscus Incorrectly
Read at the bottom of the meniscus, at eye level. Reading from the top of the meniscus or at an angle can introduce errors of 2–4 gravity points — enough to skew your ABV calculation by 0.3–0.5%.
3. Using Raw Refractometer Readings Post-Gärung
This is the single most common error we see. A post-Gärung refractometer reading of 7 °Bx does not mean your FG is 1.028. The alcohol has skewed the reading. Always apply a correction formula — see Refractometer Post Gärung Correction.
4. Confusing Apparent vs Real Vergärungsgrad
The ABV formulas above use apparent Vergärungsgrad (measured by hydrometer). Real Vergärungsgrad, which accounts for the density contribution of alcohol, is always higher. For most practical Hobbybrauen purposes, apparent Vergärungsgrad and the associated ABV calculation are what you want. Real extract calculations are more relevant for professional brewers optimising caloric content.
5. Not Accounting for Gabes
If you add sugar, honey, or fruit after taking your OG reading, you need to recalculate. The simplest approach: take a Stammwürzewert immediately before and after the addition. Alternatively, calculate the sugar contribution using known values:
| Gabe (per litre) | Ungefährer SG-Anstieg |
|---|---|
| 10 g table sugar | +0.004 |
| 10 g honey | +0.003 |
| 100 g fruit (variable) | +0.002 to +0.005 |
| 10 g Trockenmalzextrakt | +0.004 |
Choosing the Right Instrument
The accuracy of your ABV calculation depends entirely on the accuracy of your Stammwürzewerte. A quality hydrometer remains the gold standard for Hobbybrauer. For a detailed comparison of hydrometer types, precision ranges, and our recommended models at every price point, see our Hydrometer Buying Guide.
A good triple-scale hydrometer costs under 15 EUR (about $16 USD), reads in SG, Brix, and potential alcohol simultaneously, and will last for years if you do not drop it. Pair it with a tall, narrow test jar for the most accurate readings.
Fortgeschritten: Realer Extrakt und Kalorien
For completeness, here is how to calculate real extract (RE) and approximate caloric content:
RE (°P) = 0.1808 × OE + 0.8192 × AE
Where OE is the original extract in °Plato and AE is the apparent extract in °Plato.
Calories per 330 ml = 330 × FG × (6.9 × ABW + 4.0 × (RE − 0.1))
Where ABW (Alcohol By Weight) = ABV × 0.794.
| Bierstil | Typischer ABV | Approx. Calories (330 ml) |
|---|---|---|
| Light Lager | 3.5–4.2% | 95–120 |
| Pale Ale | 4.5–5.5% | 140–170 |
| IPA | 6.0–7.5% | 180–230 |
| Imperial Stout | 9.0–12.0% | 270–380 |
| Barleywine | 10.0–14.0% | 310–430 |
Summary: Picking the Right Formula for Your Brew
| ABV-Bereich | Beste Formel | Wichtige Überlegung |
|---|---|---|
| 0–6% | Standard | Simple, fast, accurate within ±0.1% |
| 6–8% | Either | Difference is marginal |
| 8%+ | Miller | Standard underestimates by 0.3–1.0%+ |
| Any (refractometer FG) | Terrill correction first, then Miller | Raw Brix readings are invalid post-Gärung |
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Methodik
The formulas presented in this article are sourced from established brewing science literature. The standard ABV formula (OG − FG) × 131.25 is a widely accepted simplification documented in John Palmer’s How to Brew (4th Edition, Brewers Publications, 2017), Chapter 8. The Miller formula originates from Dave Miller’s The Complete Handbook of Home Brewing (Storey Publishing, 1988) and has been validated against distillation-based ABV measurements in multiple homebrew club experiments.
Brix-to-SG conversion polynomials are derived from the ICUMSA (International Commission for Uniform Methods of Sugar Analysis) tables, as adapted for brewing use by Louis Bonham in Brewing Techniques (1997). The Wort Correction Factor (WCF) concept is discussed in Sean Terrill’s research published on his blog (seanterrill.com, 2011), which also produced the Terrill linear and cubic refractometer correction formulas referenced here.
The BJCP (Beer Judge Certification Program) 2021 Style Guidelines were referenced for typical ABV ranges by style. Calorie estimation follows the formula published by the ASBC (American Society of Brewing Chemists) Methods of Analysis, Beer-33. Comparative ABV data in the Standard vs Miller table was generated by computing both formulas against common OG/FG pairs and cross-referencing with published laboratory analyses from Brülosophy experiments (brulosophy.com).