Cooking, Baking & Brewing Homebrewing & Beer Terrill refractometer correlations

Refractometer Final Gravity Correction Calculator

A refractometer stops telling the truth the moment fermentation starts. Alcohol bends light more than the sugar it replaced, so a finishing reading of 6.5 °Bx is not 1.026 — it is closer to 1.013, and that gap is why finished beers get called stuck. Enter the reading you took before pitching and the one you took now, and this returns corrected final gravity, ABV and apparent attenuation using the Terrill correlations and your own wort correction factor.

Calculator

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Inputs this calculator takes, with typical values
InputWhat to enterExample
Original reading, before pitchingWhat the refractometer showed on the cooled wort, before any yeast went in.12.9 °Bx
Current or finishing readingWhat it shows now, on a degassed sample at the instrument's reference temperature.6.76 °Bx
Wort correction factorYour own instrument's factor. Measure it once against a hydrometer; 1.04 is the usual starting point.1.04
CorrelationThe cubic fits a wider range of gravities; the linear is easier to reproduce by hand.Terrill cubic (more accurate)

It returns

  • Corrected final gravity — The gravity a hydrometer would read on this sample.
  • Alcohol by volume
  • Apparent attenuation
  • Original gravity — Converted from the starting reading, where the plain sugar conversion still holds.
  • Uncorrected reading, as if it were gravity — What you would have got without correcting, shown so the size of the error is visible.
  • Size of the error — Gravity points between the uncorrected and the corrected figure.

The formula

FG=1.00000.0044993OB+0.011774FB+0.00027581OB20.0012717FB20.00000728OB3+0.000063293FB3
FG=1.00000.00085683OB+0.0034941FB
OG=1+OB258.6OB258.2×227.1

In plain text: FG = 1.0000 − 0.0044993·OB + 0.011774·FB + 0.00027581·OB² − 0.0012717·FB² − 0.00000728·OB³ + 0.000063293·FB³

  • FGCorrected final gravity (SG)
  • OBOriginal reading divided by the wort correction factor (°Bx)
  • FBFinishing reading divided by the wort correction factor (°Bx)

Both readings are divided by the wort correction factor before they enter the equation.

Updated Category Homebrewing & Beer Verified against published test cases Reading time 10 min

Why a refractometer stops being right once yeast goes in

A refractometer measures how much a liquid bends light, and it is calibrated on the assumption that the only thing dissolved in that liquid is sugar. Before you pitch, that assumption is close enough to true, so the reading converts cleanly to gravity. The moment fermentation begins it stops being true, because yeast is replacing sugar with ethanol and ethanol refracts light more strongly than the sugar it came from.

The result is a reading that is too high, and stays too high. A beer that has genuinely finished at 1.013 will often still show around 6.5 °Bx on the refractometer. Read that as a gravity and you get roughly 1.026, which looks like a fermentation that stalled halfway. Every year a large number of perfectly healthy beers get roused, re-pitched, warmed up or thrown away on the strength of that misreading.

The fix is not a different instrument. It is a correlation that takes both readings — the one from before pitching and the one from now — and returns the gravity a hydrometer would have shown. Two readings are needed because the correction depends on how much alcohol is present, and the only way to know that is to know how far the wort has come.

The two corrections, and why they are not the same thing

There are two separate adjustments here and they are routinely confused. Applying one and calling it done is the most common way this calculation still goes wrong.

The wort correction factor handles the difference between sucrose and wort. Your refractometer was calibrated in a sucrose solution, but wort contains maltose, maltotriose, dextrins and protein, and that mixture refracts a little differently. The factor is a simple divisor: your reading divided by the factor gives the true Brix. It is a property of your particular instrument and your typical wort, it applies to every reading you take including the pre-pitch one, and it is usually between 1.00 and 1.06.

The alcohol correction handles the presence of ethanol, and only applies after fermentation has started. This is the cubic or linear equation. It cannot be expressed as a single divisor because the relationship is not proportional — the distortion grows with the alcohol produced, which is why the equation needs the original reading too.

Order matters. Divide both readings by the wort correction factor first, then feed the corrected pair into the equation. Doing it the other way round, or skipping the first step because the second one looks more important, puts a few percent of error into the input of a correlation that was fitted on properly corrected data.

How to find your own wort correction factor

Use 1.04 until you have measured yours, then stop using 1.04. The factor varies between instruments and it is the single input here that you can pin down exactly with about ten minutes of work.

On your next three or four brews, take a hydrometer reading and a refractometer reading of the same cooled, well-mixed pre-pitch wort. Convert the hydrometer's specific gravity to Brix, then divide the refractometer reading by it. Average the results. That average is your factor, and it will stay usable until you change instruments or start brewing a very different kind of wort.

The reason this is worth doing is leverage: the factor divides both readings, so an error in it propagates into the original gravity, the final gravity, the ABV and the attenuation at once. A factor that is wrong by 0.02 shifts a typical original gravity by around two and a half gravity points, and the ABV along with it.

Worked example: 12.4 °Bx down to 6.5 °Bx

Take a beer that read 12.9 °Bx on the refractometer before pitching and reads 6.76 °Bx now. The instrument's measured wort correction factor is 1.04.

  1. Correct both readings. 12.9 ÷ 1.04 = 12.4 °Bx, and 6.76 ÷ 1.04 = 6.5 °Bx. Every step from here uses the corrected pair.
  2. Original gravity. The pre-pitch reading has no alcohol in it, so the sucrose conversion applies: OG = 1 + 12.4 ÷ (258.6 − (12.4 ÷ 258.2) × 227.1) = 1 + 12.4 ÷ 247.69 = 1.0501.
  3. Final gravity, term by term. Using the cubic with OB = 12.4 and FB = 6.5: the linear terms give −0.05579 and +0.07653, the square terms +0.04241 and −0.05373, the cube terms −0.01388 and +0.01738. Add them to 1.0000 and you get 1.0129.
  4. What the uncorrected reading would have claimed. Converting 6.5 °Bx straight to gravity gives 1.0257 — about 12.8 gravity points higher than the truth.
  5. Alcohol and attenuation. ABV = (1.0501 − 1.0129) × 131.25 = 4.87%. Apparent attenuation = (1.0501 − 1.0129) ÷ (1.0501 − 1.000) × 100 = 74%.

Run the same pair through the linear equation and you get 1.0121, eight ten-thousandths below the cubic. That gap is the honest measure of how much precision this calculation has: reporting a corrected final gravity to more than three decimal places is reporting noise.

Reading the result: finished, stuck, or neither

Apparent attenuation is the number that tells you whether fermentation is done, and the target depends on the yeast rather than on the beer. Most ale strains finish between 72% and 80%. Many lager strains reach 78% to 84%. Saison and Brettanomyces strains run well past 85% and occasionally past 90%. English strains are often deliberately lower, in the high 60s.

So a corrected attenuation of 74% on a beer pitched with a standard American ale strain is a finished beer. The same 74% from a saison strain is a fermentation with work left to do. Compare against the strain's published range, not against a universal number.

The far more useful test is stability. Two corrected readings taken two or three days apart that agree to within a gravity point mean fermentation has stopped, whatever the absolute figure is. A single reading — corrected or not — cannot distinguish a finished beer from one that is still slowly moving, and this is the question people most often try to answer with one measurement.

How large the uncorrected error gets

Corrected against uncorrected final gravity, for a wort that started at 12.4 °Bx corrected (OG 1.050), using the Terrill cubic.
Corrected finishing readingTrue final gravityIf read straight as gravityError, gravity points
5.0 °Bx1.00601.019613.6
6.0 °Bx1.01061.023613.0
6.5 °Bx1.01291.025712.8
7.0 °Bx1.01531.027712.4
8.0 °Bx1.02031.031811.5
9.0 °Bx1.02561.035910.3

The error is roughly ten to fourteen gravity points across the normal finishing range, which is more than enough to turn a finished beer into an apparently stuck one.

These equations are fitted for finished beer

Both correlations were derived from beers at or near terminal gravity. Below roughly 60% apparent attenuation they drift, and at zero attenuation — feeding in the same reading twice — the cubic returns a gravity noticeably below the true original, which is obviously wrong. That is not a defect in the equation, it is the equation being used outside the range it was fitted on. Mid-fermentation readings are useful for watching a trend. They are not gravities.

Where this still goes wrong

  • Skipping the wort correction factor. The alcohol equation gets the attention, so the sucrose-versus-wort correction gets dropped. It applies to both readings and it moves the answer by more than most people expect.
  • Using someone else's factor. A number from a forum post describes their refractometer, not yours. Ten minutes with a hydrometer replaces the guess permanently.
  • Reading a hot or gassy sample. Automatic temperature compensation covers a modest range around the reference temperature, not a sample straight off the boil. Dissolved CO2 scatters light and drives the reading around; degas the sample first.
  • Losing the original reading. The correction is impossible without it. If the pre-pitch refractometer figure is gone, you cannot reconstruct it from a hydrometer reading taken later — take the reading and write it down before the yeast goes in.
  • Quoting four decimal places. The two published correlations disagree by about one gravity point on the same input. Report three decimals and treat the last one as soft.

When to use a hydrometer instead

The refractometer's advantage is sample size. A few drops tells you where a fermentation is without pulling the 150 ml a hydrometer cylinder needs, which matters on a small batch and matters more when you are checking daily.

For the reading that goes on a label, a competition entry or a duty return, use a hydrometer. It measures density directly, needs no correlation, and carries no dependence on a fitted equation or on how well you measured your correction factor. The refractometer is the instrument for monitoring; the hydrometer is the instrument for the number of record.

Once you have a trustworthy final gravity, the rest follows from it: alcohol by volume, real attenuation and calories, priming sugar for the batch, and brewhouse efficiency against the grain bill. If your reading was taken warm, correct it for temperature with the hydrometer temperature calculator before you use it anywhere.

Terms used here

Brix (°Bx)
Grams of sucrose per 100 g of solution. On wort it is close to degrees Plato, and refractometer scales are usually marked in one or the other.
Wort correction factor
The divisor that converts your refractometer's sucrose-calibrated reading into true wort Brix. Instrument-specific, typically 1.00 to 1.06.
Apparent attenuation
The drop in gravity as a percentage of the original gravity above 1.000. Called apparent because alcohol lowers the density, so it overstates how much sugar was actually consumed.
Terminal gravity
The gravity at which fermentation has genuinely stopped, confirmed by two readings a few days apart that agree rather than by any single number.

Frequently asked questions

Why is my refractometer reading so much higher than my hydrometer?

Because there is alcohol in the sample. Ethanol bends light more than the sugar it replaced, so once fermentation starts the refractometer reads high and keeps reading high. On a typical finished beer the gap is ten to fourteen gravity points. The hydrometer is right; the refractometer needs the correction on this page before its reading means anything.

Do I really need the original reading, or can I just correct the current one?

You need both. The size of the alcohol distortion depends on how much alcohol is present, and the only way to know that is to know how far the gravity has fallen. A correction that used only the current reading would have to assume an attenuation, which is the very thing you are trying to measure. If you did not record the pre-pitch refractometer reading, this calculation cannot be recovered.

What wort correction factor should I use if I have not measured mine?

Start at 1.04, which sits in the middle of the usual 1.00 to 1.06 range, and replace it as soon as you can. Take a hydrometer and a refractometer reading of the same cooled pre-pitch wort on your next few brews, convert the hydrometer figure to Brix, divide the refractometer reading by it, and average. That number is a property of your instrument and will not need revisiting.

Should I use the cubic or the linear equation?

Use the cubic unless you need to reproduce the arithmetic by hand. It fits a wider range of gravities. On a normal finished beer the two agree to about one gravity point, so the choice rarely changes a decision — and that agreement is a fair guide to how precise this correction can be at all.

Can I use this mid-fermentation to see whether the beer is stuck?

You can watch the trend, but do not trust the absolute number. Both correlations were fitted against finished and near-finished beer, and below roughly 60% apparent attenuation their accuracy falls away. The reliable stuck-fermentation test is two corrected readings a few days apart: if they agree, fermentation has stopped, whatever the number says.

My corrected attenuation came out above 100%. What went wrong?

Attenuation above 100% means the corrected final gravity landed below 1.000. That is genuinely possible in a very dry cider, mead or fully attenuated saison. In an ordinary beer it almost always means the wort correction factor is too high, which pushes the original reading down and the calculated drop up. Re-measure the factor before believing the result.

Does automatic temperature compensation handle a warm sample?

Only within a modest band around the instrument's reference temperature, and only after the sample and prism have equilibrated. A drop straight off a hot fermenter will read wrong regardless of the ATC label. Let the sample reach room temperature, and give it a few seconds on the prism before reading.

What final gravity should I be aiming for?

There is no universal figure — it depends on the yeast and the wort. Most ale strains land between 72% and 80% apparent attenuation, many lager strains between 78% and 84%, and saison or Brettanomyces strains above 85%. Check the strain's published range and compare against that. A gravity that is stable across several days matters more than hitting a specific target.

References

  • Refractometer Estimates of Final GravitySean Terrill
  • How to Brew, 4th edition — John J. Palmer, Brewers Publications, 2017
  • Principles of Brewing Science, 2nd edition — George Fix, Brewers Publications, 1999
  • Methods of Analysis — Beer: specific gravity, extract and alcohol — American Society of Brewing Chemists