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Refractometer FG Results

Last time I wrote about refractometry in brewing, I had developed a correlation for determining FGs from refractometer readings that, in my own brewing, seemed to be an improvement on the correlation used in (to the best of my knowledge) all contemporary brewing software, spreadsheets, etc. A total of eight brewer-instrument pairs contributed additional data for analysis: six volunteers in addition to myself, using both my own instruments and those at the brewery. The data submitted included four beers with very low attenuations, which I’m somewhat arbitrarily defining as anything below 50% RDF (61% ADF). Neither the old nor new correlations gave results even close to the measured FG values. I attempted to incorporate these beers into the correlation, but was unable to maintain accuracy for more typical worts while doing so. Removing those beers from the data results in 68 independent triplets, which were used to compare the standard refractometer correlation to two curves fit using the same twelve data points as before. First, a simplified cubic:

FG = 1.0000 – 0.0044993*RIi + 0.011774*RIf + 0.00027581*RIi² – 0.0012717*RIf² – 0.0000072800*RIi³ + 0.000063293*RIf³

And a linear polynomial:

FG = 1.0000 – 0.00085683*RIi + 0.0034941*RIf

A statistical analysis of the results makes it clear just how inadequate the original correlation was: it consistently under-estimates the FG, albeit not as much as in my own brewing. I assume that’s due to the average attenuation in the complete data set (62% RDF) being closer to the typical values assumed by the old correlation, as I noted in my first post on the subject. It is also noticeably less precise than even the relatively poor “triple scale” hydrometers used by most home brewers, let alone one designed for FG readings. Interestingly, the linear correlation is more accurate than the cubic, albeit slightly less precise. Both compare favorably to a consumer-grade hydrometer – which with perfect use could potentially be read to ±0.0005 SG.

I find it a little easier to understand when the data are presented graphically:

So it seems that – with the exception of very low-attenuating worts – either of the new correlations can provide accuracy and precision on par with the consumer-grade hydrometers typically used by home brewers. In a situation where a new correlation was being substituted for the old one, the cubic fit may be preferable since it only requires the coefficients to be altered. Otherwise, in my opinion, the linear fit provides wholly acceptable results. As always, though, your mileage may vary. In situations where the FG needs to be known precisely, testing with a properly calibrated precision hydrometer remains the best option.

I’ve updated my FG prediction spreadsheet to version 3.0, which, in addition to the two new correlations, incorporates a more accurate Brix-to-OG conversion, and reverts the default “wort correction factor” to 1.04, which would seem to be more typical for the overall data set. Download links are below.

Finally, I’d like to thank Dave, Enid, Gustav, James, Kai, and Scott for recording and sharing their data.
 
 
Update: 06 Jan 2012

I’ve (finally) written a PHP version of the basic FG calculation, so that people can use it without downloading the spreadsheet.
 
 
Spreadsheet download:
fg_calculator_v3.0.ods | fg_calculator_v3.0.xls

60 comments to Refractometer FG Results

  • Alan Taylor

    Sean,

    Great work; thanks for doing all this. Although as an English professor, I’ll just have to trust your math.

    Questions:

    1) I heard a podcast you did with James Spencer wherein you remarked that refractometers on the market thatinclude a specific gravity scale are flawed in that the temperature correction was not applied to the scale. That was several years ago; is that still the case? If so, is there some way of getting a more accurate result? Or should I just rely on Brix to be safe? (I have been using a refractometer that I purchased from Northern Brewer that has a specific gravity scale).

    2) Is the attached spreadsheet here just about collecting the data and showing the accuracy of your new formula? Or is the ABV in your spreadsheet the more reliable ABV using your formula?

    Thanks,

    Alan

    P.S. Thanks for providing a spreadsheet in an open source format!

    • 1) I think that podcast aired in August or September of last year, actually. At any rate, as far as I know there are still no accurate SG-graduated refractometers on the market. For a quick check, look at what SG corresponds to 25°Bx. It should be about 1.106. If it’s more like 1.100, they used the “multiply by four” rule, and the SG scale won’t be accurate above about 1.050. By the way, this is a completely separate issue from temperature compensation – when I talk about hydrometer and refractometer readings, always assume that any temperature correction needed for your instruments has already been applied.

      2) The ABV value given by the spreadsheet should be more accurate than the simpler formulas most people use (i.e. 131*(OG-FG)). It’s still just an approximation, though. If you need to know the ABV more precisely than a few tenths of a percent, you’ll have to have your beers tested.

      I love getting comments from high-functioning English speakers, by the way. People just don’t use “wherein” enough.

      Cheers,
      Sean

  • [...] other. Everyone I know of who's tried both has found the standard correlation to be less accurate. http://seanterrill.com/2011/04/07/refractometer-fg-results/ __________________ http://seanterrill.com/category/brewing/ [...]

  • Fred L. Johnson

    Sean:

    Many thanks for some good work. The homebrewing community needs lots more of this kind of work!

    Would you please comment more on the “wort factor” value. I have not heard using this in correcting the Brix scale.

    Also, why you believe you are getting a value (1.02) that is different than the value (1.04) that has been assigned to wort in the past. I would expect your wort sugar profile to be similar to others historically, and unless the protein content of your wort is substantially different from others, I would expect little difference. Perhaps you simply believe the old value was not a very good one. Correct?

    • Fred,

      The reason a wort correction factor is necessary is that refractometers are most typically used in the wine industry, so they’re calibrated to measure simple sugar solutions. Wort is a little more complex, being mostly maltose, maltotriose, etc., each of which has its own slightly different refractive index in solution. As far as why my worts have a slightly different correction factor, I would guess that I tend to brew more attenuative worts than most (81% ADF for this data set), which would therefore contain a higher proportion of simpler sugars.

      Sean

  • Fred L. Johnson

    Sean:

    I see that your formulas above use RI, but in fact your spreadsheet uses the coefficients in the formula with Brix, not RI. Am I missing something, or is this an error in the formulas above?

    • Fred,

      The reason I wanted to use the “RI” nomenclature in the formulas is to make it clear that the inputs are the refractometer readings, not the actual density of the wort in degrees Brix. When using the spreadsheet, no other corrections or calculations need to be done.

      Sean

  • [...] Originally Posted by Shaneoco1981 Do you guys know where I might be able to get the calculations for future reference? He was just on Basic Brewing Radio talking about how he's improving on the current formulas. http://seanterrill.com/2011/04/07/refractometer-fg-results/ [...]

  • [...] new formula. The details of the formula, along with an easy to use spreadsheet can be found here: http://seanterrill.com/2011/04/07/refractometer-fg-results/ Any statistics/math people looked into this? Has anyone done their own testing of his new formula? [...]

  • Hi Sean,
    This is an email I sent to James Spencer because he had asked to send him some feedback once I had a chance to take a post-fermentation reading. cheers.

    I racked a beer today and was able to run some calcs.

    Original SG was 1.085 which would have been 21 brix. (I did not record this but it would either be 20.5 or 21 based on using a few tools).

    Final SG was 1.015 and final brix was 9.5.

    A couple of the calculators on the internet said my SG would be either 1.007 or 1.008 based on the final brix reading of 9.5 (I did not input the SG reading of 1.015).

    But his calculator said that my SG reading would be 1.0146, or…. 1.015, which is what it was! (if I am looking at the correct column, “New Linear.”)

    So I would say that yes, his calculator gave me a more correct SG reading when I inputed the final brix reading (as well as the original ones).

    I guess that means I might be able to rely on brix readings for fairly accurate SG values, but what sample am I supposed to drink?! :)

    cheers

    don

    • Thanks Don. That’s good to hear.

      As far as tasting the gravity samples, well, I’ll take an extra half pint of finished beer over a warm, flat one any day. ;)

      Cheers,
      Sean

  • [...] (57) Popular PostsRefractometer FG ResultsToward a Better Refractometer CorrelationYeast Pitching Rate ResultsYeast Ranching and YouTHA [...]

  • [...] Sean Terrill was recently on Basic Brewing where he discussed his efforts to create an improved FG correction formula for refractometers. His formula seems to be a marked improvement but there's still loads of caveats. Have a listen. __________________ Many Bothans died to bring you this information. [...]

  • [...] reading. Every other spreadsheet/site that I've seen uses a demonstrably inaccurate formula. http://seanterrill.com/2011/04/07/refractometer-fg-results/ __________________ http://seanterrill.com/category/brewing/ [...]

  • [...] this spreadsheet, it's given me more accurate results than the MoreBeer one. __________________ The [...]

  • [...] He has created a correction sheet that he claims comes up with a more accurate FG reading. http://seanterrill.com/2011/04/07/refractometer-fg-results/ For what it is worth I was getting FG readings that were unnaturally low on many batches with my [...]

  • [...] so that I can adjust my recipes accordingly. A refractometer will be useful here and thanks to recent research by Sean Terrill it also may be used to measure final gravity with respectable [...]

  • [...] enough makes no difference Plato). You need to compensate for the unfermented sugars to get SG. http://seanterrill.com/2011/04/07/refractometer-fg-results/ Thanks for that spreadsheet. I like it over the other one I use. __________________ [...]

  • Erik Todic

    Hello,
    I am searching for a spreadsheet like yours, with compensation for alkohol, but with oechsle (OG and FG) all the way. In sweden it´s common to have a refractometer in oechsle. I know that I easely can covert oechsle (OG) to Brix by dividing it with 4, but it would be great to have your spredsheet modified to the rigt unit from the start. Are you interested in modifying your spredsheet to oechsle? Thanks for a great tool.
    Regards
    Erik

    • Erik,

      My concern with releasing a version of the sheet that uses SG (or Oechsle) readings is that there are refractometers on the market (in the US, at least) with an inaccurate SG scale, in addition to the °Brix scale. If you want to modify the sheet, the easiest way would probably be to insert new columns for the Oechsle readings, and use this formula in the °Bx fields to convert:

      = -463.37 + 668.72*(1 + 0.001*O) - 205.347*(1 + 0.001*O)^2

      Where O is the Oechsle reading.

  • [...] (61) Popular PostsRefractometer FG ResultsRefractometer Estimates of Final GravityBuild a Better StirplateToward a Better Refractometer [...]

  • Randy Simmons

    Ok.
    Here is what I don’t get…
    I have always used the “MoreBeer spreadsheet”.

    The FG calculations (which I thought is what Sean spent so much time doing the research on) is coming out almost exactly the same using the MoreBeer spreadsheet or Sean’s.
    So am I to assume the MoreBeer one was already using Sean’s formula (or one that is just as good) ???

    The big DIFFERENCE that I am seeing is with the OG !!!???

    I THOUGHT there was some “universal” formula for converting BRIX to GRAVITY if NO alcohol is present ?

    The MoreBeer spreadsheet uses:
    =1.000019+0.003865613*(A7)+0.00001296425*(A7*A7)+0.00000005701128*(A7*A7*A7)
    where A7 is the OG in BRIX
    And Sean’s spreadsheet uses:
    =((C7/$E$3)/(258.6-(((C7/$E$3)/258.2)*227.1))+1)
    where C7 is the OG in BRIX and $E$3 is the “wort correction factor”

    What the heck is the “Wort Correction Factor” ??

    If I set the “Wort Correction Factor” to 1.0, instead of the default 1.04, then I get the same OGs that the MoreBeer sheet gives.

    So maybe I didn’t understand… Is this “wort correction factor” and determining OG (not FG) what you did all the research on !??!?

    • Randy,

      There are any number of formulas to convert SG to °Plato and vice versa. I haven’t encountered the one from the MoreBeer sheet before, and it could be that they did their own curve-fitting to generate it. Regardless, I plugged in a few values and it seems to give good results. The formula I used comes from de Clerck, by the way.

      The “wort correction factor” is the offset that needs to be applied in order to correct the refractive index of wort (mostly maltose) to that of sucrose. Since the refractometers we’re talking about were designed for the wine industry, they’re calibrated to the refractive index of a pure sucrose solution. So apparently the MoreBeer sheet expects the user to do the wort correction by hand, prior to using the spreadsheet. There’s some merit to that approach, since the correction will be slightly different for each wort. But the factor of 1.04 is well-established, and based on the data I’ve collected it seems to be a good average.

      As far as comparing the results of the two equations for FGs, I did find in my early research that the old correlation gives good results for a fairly narrow attenuation range, around 70% ADF. So if your worts tend to attenuate around that level, you may not see a substantial improvement when using the new correlation. My spreadsheet does give the results of both equations, so that you can keep track and see for yourself which gives the best results in your brewing.

      Cheers,
      Sean

  • [...] have their opinions, based on their experiences. I've found Sean Terrill's recent formula to be quite decent, always within a point or so of my hydrometer. YMMV __________________ [...]

  • Steve da sleeve

    Hello – thanks for this spreadsheet, it really helped one day when I broke not one but two hydrometers within 5 minutes and had nothing but my refractometer to measure the FG! Anyhoo I used it again today with a seemingly hand calibrated hydrometer and the FG was off by 0.0001 (1.008 vs 1.0081!) The OG calculated on the spreadsheet however was inaccurate. I measured 15 brix and 1.0062 the spreadsheet calculated 1.059. I’m not sure what this means but there you have it! Oh and if you wish more data I can provide it unless/until I break this new hydrometer, just let me know.

  • Tyler

    Sean,

    This is awesome… just what I was looking for with the new refractometer I got for Christmas. :-)

    Just a an FYI… I think I found the location of the original formula online. It was done by a winery, Valley Vinter, and here is the experiment that created the formula.

    http://www.valleyvintner.com/Refrac_Hydro/Refract_Hydro.htm

    Tyler

  • [...] he did, but I'm sure the corrections in Beersmith are bad! See this for loads more info: (http://seanterrill.com/2011/04/07/refractometer-fg-results/) [...]

  • I was listening to the podcast on Basic Brewing again today (I actually have a refractometer now so the data and info are much more valuable). You state that there are extremes for which your equations don’t work well. I see the 51% attenuation, but what are the other extremes? How high OG? How low OG? How high ABV? How low ABV? How high attenuation? I have an Imp Stout that started @ 1.105 and FG 1.024 for 10.5% ABV, is that beyond the scope? I have a Blonde w/ OG 1.037, and FG 1.009, is that too low (this one is all from refractometer and using your conversions). Thanks for the help.

    • Justin,

      The twelve data points used to develop the correlation had OGs from 1.036 to 1.106, FGs from 1.007 to 1.022, and ADFs from 73% to 91%. As long as you stay in those ranges, the results should be fairly accurate. If one or more of them gets near the margins, though, you may get better results from a hydrometer. It all depends on what kind of precision you want/need.

      Just as an example, I recently brewed a Belgian Blonde with an OG of 1.041 and an FG of 1.005. The OG and ADF (88%) are both in range, but because they’re both near the margins the correlation didn’t give very accurate results (estimated FG was 1.009). I would guess that both of your beers would give good results, because the gravities are marginal but the attenuations are more typical. Again, it just depends on what you personally consider acceptable.

      Cheers,
      Sean

  • [...] off… But I am going to be using this guys correction XLS sheet for converting from Brix to SG. http://seanterrill.com/2011/04/07/refractometer-fg-results/ GA_googleFillSlotWithSize("ca-pub-3927874040083090", "HomeBrewTalk_Forum_336x280_BTF", 336, [...]

  • [...] alcohol. Here's a link to someone who has been working on tweaking his calculation for awhile. http://seanterrill.com/2011/04/07/refractometer-fg-results/ Scroll down to just before the comments section for the spreadsheet link. [...]

  • [...] (and I purchased one), I wasn't aware any calculations had to be done. I found a spreadsheet here. If I'm using it properly, I think my real FG is 1.013? I ballparked 9.8 Brix starting and 6 Brix [...]

  • [...] with it, I find his spreadsheet to correct for readings I used to get that were too low. http://seanterrill.com/2011/04/07/refractometer-fg-results/ GA_googleFillSlotWithSize("ca-pub-3927874040083090", "HomeBrewTalk_Forum_336x280_BTF", 336, 280); [...]

  • [...] Quite close to each other, but also quite a bit higher than the Apparent Extract. So the sugar content of this fermented beer is the same as the sugar content of a ~5.6° P unfermented wort. This is also the reason why a 10% Imperial Stout with an FG of 1.020 is much sweeter than a 3.5% Pale Ale with an FG of 1.020. Of course other factors influence sweetness as well, such as ethanol content (can give a sweet flavor), types of malts used, any spices used, and bitterness. So, don’t blindly trust your hydrometer as a measure of sweetness! Refractometers are of course a whole other story, that I won’t be getting in to, instead have a look at this and this. [...]

  • [...] plan to analyze my measurements at a later time when I have enough data). This may be helpful: http://seanterrill.com/2011/04/07/refractometer-fg-results/ googletag.display('div-gpt-ad-1352476986422-7'); __________________ [...]

  • [...] post ferment Brix readings to gravity readings that I have found is produced by Sean Terrill. See http://seanterrill.com/2011/04/07/refractometer-fg-results/ for details. He even provides spreadsheet templates for your convenience. Personally, if there's [...]

  • [...] corrects refractometer readings post fermentation. It's the most accurate one I've seen….. http://seanterrill.com/2011/04/07/refractometer-fg-results/ googletag.display('div-gpt-ad-1360174805302-5'); __________________ Life begins at 60….1.060, [...]

  • Martijn

    Hi Sean,

    Thanks for your amazing work!

    I’m trying to build my own calculator (with a user interface designed for mobile, so I always have the calculation at hand on my phone), and I want to be able to enter (also) SG values. My hydrometer SG scale seems to be correct (definitely not brix * 4), and I’m more used to using SG values. Anyway, above you presented the formula:

    -463.37 + 668.72*(1 + 0.001*O) – 205.347*(1 + 0.001*O)^2

    to convert SG to Brix. But shouldn’t this formula also include the wort correction factor to be precise? Ie. shouldn’t the Brix-to-SG and SG-to-Brix formulas be each others opposites? And if so, would you be so kind to include it in the formula for me? If not I guess I will be dusting off my math skills. :-)

    Thanks,
    Martijn

  • Martijn

    Wait a minute, with regard to my last comment. Only now I realize that I don’t really need to “dust off my math skills” to realize it would just require multiplying the entire result of that formula by the wort correction factor. Nevermind and thanks again!

  • [...] is the best correction chart I've found…. http://seanterrill.com/2011/04/07/refractometer-fg-results/ googletag.display('div-gpt-ad-1360174805302-5'); __________________ Life begins at 60….1.060, [...]

  • Hi Sean,
    great tool! I was wondering why you’re using your simplified cubic polynomial in your calculator after all, since your data clearly suggest that the new linear calculates final gravities that are more closely to the actual hydrometer readings? (even though the differences between the two “Terrills” appear to be marginal). Thanks in advance.
    Sandro

    • Sandro,

      The reason I prefer the cubic correlation is that while for this particular dataset it was less accurate, it was still more precise (smaller standard deviation), which leads me to believe that it will be more accurate in the long run. For what it’s worth, for the data I’ve taken over the past two years (27 beers), the cubic is both more accurate and more precise.

      Sean

  • [...] and well researched. Probably, nb is using a more basic equation. Check this out for more info: http://seanterrill.com/2011/04/07/refractometer-fg-results/ [...]

  • [...] like my refractometer for OG AND FG. I read this article by Sean Terrill in regards to a correlation for determining FGs from refractometer readings. I have been using his [...]

  • [...] För att få lite redundans i mätningarna och för att slippa fiska upp så mycket öl ur jäshinken valde vi också att införskaffa en refraktometer. Hittade en intressant artikel om omvandlingsformler för att kunna använda refraktometern för att mäta FG här [...]

  • Henric

    Hi Sean,

    Can you comment on the formulas used by your spreadsheet to calculate ABV? I seem to get rather different results than with other calculators when I plug in OG/FG from your sheet.

    For example, a beer with Orig Brix 20,8 and Final Brix 11,9 gets and ABV of 7.4% with your sheet. Plugging in the New Cubic FG (which appears to be used in the ABV calculation) and the calculated OG into http://www.brewersfriend.com/abv-calculator/ gives 7.61% and 8.23% respectively, depending on the formula used. BeerSmith gives an ABV of 7.7% with the same SG readings.

    Many thanks,
    Henric

    • Henric,

      I use Balling’s formula:

      ABW = 0.8192 * (OG – FG) / (2.0665 – 0.010665 * OG)

      With units of degrees Plato, and then multiply by 1.25 to get ABV. This does seem to give more accurate results, particularly for higher-gravity beers. My guess would be that higher-gravity worts generally have higher oxygenation and/or pitching rates, and so less alcohol than an equation based purely on attenuation would suggest. It is interesting that the second Brewer’s Friend equation takes the opposite approach, though that could make sense if the higher-gravity beers have lower pitching rates, which is probably the case for a lot of home brewers.

      Sean

      • Henric

        Hi Sean,

        I did some additional digging, as it bothered me a bit that calculated ABV varies so much between common formulas. I found a few interesting things:

        1) The “High gravity formula” used by Brewer’s Friend is based on a very good article by Michael L Hall (http://www.homebrewersassociation.org/attachments/0000/2497/Math_in_Mash_SummerZym95.pdf). However, the actual formula used is not the most accurate one provided by Michael, but one based on the simplified extract formula E=1000*(SG-1)/4. For higher gravities this extract formula becomes quite inaccurate.

        Michael instead provides a curve-fitted cubic formula which produces results very close to DeClerk’s quadratic formula (the one you are using) for extract calculation.

        For example, a brew with OG 1.070 and FG 1.015 has the following calculated OEs:
        DeClerk: 17.06
        Hall: 17.03
        Hall (simplified): 17.50

        Since Brewer’s Friend uses the last formula the calculated ABVs will be way too high for high-gravity brews.

        Another major difference is that Hall reports that the common formula for calculating RE from OE and AE (RE = 0.8192 AE + 0.1808 OE) is inaccurate, as it assumes that the attenuation coefficient is calculated at an OE of 0. Hall instead proposes the following equation:

        RE = 0.8114 AE + 0.1886 OE

        Hall then uses Balling’s formula for ABW:

        ABW = (OE-RE)/(2.0665-0.010665 * OE)

        Finally, the formula used by Hall for calculating ABV from ABW is

        ABV = ABW * (FG/0.794), rather than
        ABV = ABW * 1.25

        For the example brew above, we get the following ABVs using the various formulas:
        Balling (with ABV=1.25*ABW): 7.19%
        Balling (with revised ABV formula): 7.35%
        Hall (simplified extract formula): 7.59%
        Hall (cubic extract formula): 7.27%

  • Henric

    Hi Sean,

    Another thought: your spreadsheet seems to sum each column and divide by the number of values to calculate the mean discrepancy. Is this really the best metric when comparing different formulas?

    For example, the calculated FG using a particular formula could be 10 points high for one batch and 10 points low for the second, but the calculated discrepancy would indicate that the formula was dead on. Would it not be better to compare the sum of the absolute values of the differences between predicted and hydrometer FG?

    /Henric

    • It is a fairly arbitrary definition. I prefer the mean value approach because it focuses on accuracy rather than precision, and for FG estimation I feel that’s more important. In practice, it wouldn’t make much difference, since the new equations appear to be both more accurate and more precise.

      Sean

  • Sandro

    Hi Sean,

    I started collecting data (similar to your experiment) from German home brewers and I found that the old cubic formula is much more accurate if you do NOT correct the Rf values with the wort correction factor (the Ri values require correction though). Unfortunatly I couldn’t find an original reference to the old cubic, but perhaps the way you have been using it was wrong to start with???? Nevertheless, for the data I collected so far the “Linear Terrill formula” is closest to the hydrometer readings being still more accurate than the Ri-only corrected old cubic formula. The Ri and Rf corrected old cubic is way off the mark.

    Regards
    Sandro

    • Thanks Sandro, that’s good to know. Unfortunately, I never have found any information or documentation for the “old cubic” formula. It’s entirely possible the WCF is only intended to be applied to the RIi values. For the data I do have, adjusting the corrections as you did improves the fit, though only by 0.0007 SG on average. If you’re able to share the data you collected, I’d love to incorporate it. You can always email me at sean@seanterrill.com

      Cheers,
      Sean

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