Alcohol by volume is not measured directly in a home or small-scale setting. It is inferred from density. Sugar dissolved in water makes the liquid denser than water; fermentation converts that sugar into ethanol, which is markedly less dense than water; so the drop in density between the start and the end of fermentation is a proxy for how much ethanol was produced. The ABV calculator above turns a pair of gravity readings into that figure, using the published formulas rather than a single hidden constant.
Arb Digital builds free calculators for the arithmetic that sits between a measurement and a number people record. This page is about the measurement itself: what a hydrometer actually tells you, why two accepted formulas disagree by a few tenths of a percent, and where the reading goes wrong before the arithmetic ever gets a chance to. It is a measurement tool and nothing else — there is no guidance here about drinking, serving or consumption of any kind.
What This ABV Calculator Does
Enter an original gravity and a final gravity, in either specific gravity or degrees Brix, and the tool returns alcohol by volume on the formula you select. It also reports alcohol by weight, apparent attenuation, the raw gravity drop in points, and the result the extended formula gives, so you can see how far the two methods diverge on your particular readings.
The Brix option converts to specific gravity first using the standard cubic approximation, because every ABV formula in general use is written in terms of specific gravity. That conversion is itself an approximation fitted to sucrose solutions, and it is accurate enough for practical work while not being exact for a wort or a must containing other dissolved solids.
One boundary worth stating plainly. This page derives an ABV from fermentation readings. It does not convert a known ABV and a served volume into standard units of alcohol, which is a completely different calculation performed on a finished, labelled product — our alcohol units calculator handles that. Use this tool when you have gravity readings and no ABV; use the other when you have an ABV and no gravity readings.
How to Use It
- Record the original gravity before fermentation begins, after the liquid is thoroughly mixed. An unmixed sample reads whatever happens to be at the sampling point rather than the average.
- Record the final gravity once fermentation has finished and the reading has been stable across two or three days. A falling reading means the calculation is premature.
- Match the units. Select specific gravity or Brix to match the instrument you used, and enter both readings on the same scale from the same type of instrument.
- Choose a formula. The standard multiplier is the usual choice for lower gravities. The extended form is the one to prefer when the drop is large.
- Read the attenuation figure as a sanity check. A value far outside the usual range for what you are making usually indicates a measurement problem rather than an unusual fermentation.
The Formulas and How They Are Calculated
The formula most widely quoted is a single empirical multiplier applied to the gravity difference:
ABV = (original gravity − final gravity) × 131.25
With the values loaded above, 1.055 minus 1.012 is 0.043, and 0.043 × 131.25 = 5.64 percent. The wine convention substitutes 136 for 131.25, giving 5.85 percent on the same readings, which is a reminder that the constant is a fitted approximation rather than a physical law.
The extended formula, which tracks laboratory measurements more closely at higher strengths, is:
ABV = 76.08 × (OG − FG) ÷ (1.775 − OG) × (FG ÷ 0.794)
On the same figures: 76.08 × 0.043 ÷ 0.720 = 4.544, multiplied by 1.012 ÷ 0.794 = 1.2746, giving 5.79 percent. The two differ by about 0.15 percentage points here and diverge further as the gravity drop grows, which is why both are shown rather than one being presented as the truth.
Alcohol by weight is derived from ABV using the density of ethanol relative to the finished liquid: ABW = ABV × 0.789 ÷ final gravity, giving 4.40 percent here. Apparent attenuation is the proportion of the original extract that fermented out, (OG − FG) ÷ (OG − 1) × 100, which is 0.043 ÷ 0.055 = 78.2 percent. Gravity drop is simply the difference expressed in points, so 0.043 becomes 43 points.
Why the Reading Goes Wrong Before the Maths Does
Every source of error in this calculation is upstream of the arithmetic. A hydrometer is calibrated at a specific temperature, and the reading it gives at any other temperature is wrong in a predictable direction: a warm sample is less dense, so the instrument sits lower and reads low. The definition of specific gravity as a density ratio at a stated reference temperature is set out by the US Alcohol and Tobacco Tax and Trade Bureau's explanation of specific gravity, and the practical consequence is that readings taken at wildly different temperatures should not be subtracted from one another without correcting both to the same basis.
Dissolved carbon dioxide is the second problem, and it always pushes final gravity the wrong way. A fermenting or freshly finished liquid is saturated with gas, and bubbles clinging to the hydrometer stem add buoyancy that reads as extra density. Degassing the sample before reading it removes a source of error that is easily worth several tenths of a percent on the final figure.
The third is surface tension and parallax. A hydrometer is read at the level of the liquid surface, not at the top of the meniscus that climbs the stem, and the difference is large enough to matter on the 0.001 divisions these calculations depend on. Reading at eye level in a clean trial jar rather than in the fermenter removes both errors at once. Our temperature converter is useful when the instrument is calibrated in Fahrenheit and the record is kept in Celsius, and the density converter handles conversion between density units when a datasheet uses something other than specific gravity.
Attenuation, Stuck Fermentations and What the Number Cannot See
Apparent attenuation is the more diagnostic of the two headline numbers. It describes how much of the original extract disappeared, and it varies systematically with the yeast strain, the sugar composition of the starting liquid and the fermentation temperature. A juice fermented with a strain that consumes nearly all available sugar attenuates far more completely than a wort deliberately mashed to leave unfermentable dextrins behind, and the two will produce very different attenuation figures at identical quality.
Where attenuation is unexpectedly low and the gravity has stopped falling, the standard diagnosis is that fermentation has stalled rather than finished. The University of California, Davis department of viticulture and enology publishes a technical guide to problem fermentations that sets out the recognised causes, most of which are about nutrient availability and temperature rather than anything the calculator can detect. An ABV computed from a stalled fermentation is a real number describing an incomplete process, not an error.
It is also worth being clear about what the word apparent is doing. The final hydrometer reading is depressed by the ethanol present, so it understates the sugar that genuinely remains. Real extract, the figure a laboratory obtains after distilling the alcohol off, is always higher than apparent extract. Every attenuation figure you will see quoted casually is the apparent one, and the two should not be compared with each other.
Precision, Rounding and Record Keeping
A gravity difference of one point, which is 0.001, moves the standard ABV result by about 0.13 percentage points. Since a hydrometer read by eye is realistically good to about one point, quoting an ABV to three decimal places implies a precision the instrument does not have. Two decimal places is the sensible convention for a written record and one is defensible.
That sensitivity also explains why the choice of formula matters less than people assume. Between the standard and extended forms the gap on a modest fermentation is comparable to the measurement uncertainty itself. On a large gravity drop the gap widens well beyond it, which is the point at which choosing deliberately becomes worthwhile. The formal traceability of the underlying units is maintained by the NIST Office of Weights and Measures, which is also where the calibration standards behind laboratory hydrometers ultimately lead.
For the record itself, note both raw readings, the instrument type, the sample temperature and the formula used, not just the answer. A bare ABV figure cannot be rechecked; the readings behind it can. The percentage calculator is quick for related proportional work, and the volume converter and density calculator cover the batch arithmetic that usually accompanies these records.
Arb Digital publishes hundreds of free calculators across food, finance, health and maths — no sign-up, no limits. If the one you need is missing, tell us and we will look at building it.
Browse All Free Tools Suggest a ToolCommon Mistakes to Avoid
- Taking a final gravity with a refractometer — ethanol alters the refractive index, so the instrument reads high on any fermented sample unless the result is put through a separate correction.
- Comparing readings taken at different temperatures — a hydrometer is calibrated at one temperature and reads low in a warm sample. Correct both readings to the same basis before subtracting.
- Reading through the meniscus — the value is taken at the flat surface of the liquid, not at the top of the curve climbing the stem. On 0.001 divisions the difference is not negligible.
- Calculating before the gravity is stable — a reading that is still falling gives an ABV for an unfinished fermentation. Two or three matching readings across several days is the usual test.
- Quoting three decimal places — one gravity point moves the answer by roughly 0.13 percentage points, so the extra digits imply a precision the instrument cannot deliver.
Related Free Tools From Arb Digital
Convert a finished product's stated strength and serving volume into standard measures with the alcohol units calculator, switch instrument scales with the temperature converter and the density converter, and handle batch volumes with the volume converter. The density calculator covers mass and volume relationships directly, the percentage calculator is useful for proportional adjustments, and the sourdough hydration calculator applies the same kind of ratio arithmetic to another fermentation. Everything else is on the free online tools hub.
Frequently Asked Questions
The most widely used form is alcohol by volume equals the original gravity minus the final gravity, multiplied by 131.25. The multiplier is an empirical constant fitted to typical fermentation strengths rather than a physical constant, which is why other values such as 136 appear in wine practice.
Because both are approximations of a relationship that is not linear. The simple multiplier is fitted around moderate gravity drops and drifts at higher strengths, while the extended formula includes terms that track the curve better. The gap widens as the gravity drop grows.
Not directly. Ethanol changes how the sample refracts light, so a refractometer reads high on anything that has fermented. The reading has to be put through a dedicated correction that uses the original gravity as well. A hydrometer avoids the problem entirely.
A hydrometer is calibrated at one reference temperature. Warm liquid is less dense, so the instrument floats lower and reads low, and cold liquid produces the opposite error. Readings taken at different temperatures should be corrected to a common basis before being subtracted.
It is the share of the original extract that fermented away, calculated as the gravity drop divided by the original gravity's excess over water. It is called apparent because the ethanol present depresses the final reading, so it overstates how much sugar has actually gone.
The standard route is a cubic approximation fitted to sucrose solutions, which the calculator applies automatically when you select Brix. It is accurate enough for practical work but not exact for liquids containing other dissolved solids alongside sugar.
It expresses ethanol as a proportion of the liquid's mass rather than its volume. Because ethanol is less dense than water, the figure is always lower than ABV, and it is derived here by multiplying ABV by 0.789 and dividing by the final gravity.
A single gravity point of 0.001 shifts the standard result by about 0.13 percentage points, and an instrument read by eye is realistically good to about one point. Two decimal places is the sensible convention, and three implies precision the measurement does not support.
This calculator applies published formulas to gravity readings you supply and is provided for general reference and record keeping only. Results are estimates derived from density measurements, not laboratory analysis, and where a figure is required for labelling, sale or any regulatory purpose it must be established by an accredited laboratory in line with the rules of the relevant authority.
