OK looks like we're both misunderstanding
For my part, I misunderstood your comment about the hydrometer reading converting to 5.12. This gives a totally different value then the ABV scale on a hydrometer, so ignore my comments on converting the ABV reading to Brix.
When using the Brewers Friend calculator, you need to click on the "update" button when you have the original and final gravities entered. This will give you an estimated ABV of 4.33% not 5.12% using the standard calculation.
Now, if I understand you correctly, you have only used the refractometer on a sample of wort that had been fermented and turned into beer, and tried to make sense of the refractometer vs hydrometer readings at this point. Unfortunately this will not be accurate as the fermentation process converts sugars into alcohol, and the presence of alcohol interferes with the conversion from Brix to SG.
Here are my recommendations for using and checking the accuracy of a refractometer, combined with an explanation of how a refractometer works. I use Brewers Friend calculators to assist as I have checked them for accuracy.
- A hydrometer measures the relative density of a solution (i.e. the density of that solution relative to that of water), while a refractometer measures the refractive index of a solution (i.e. the degree by which that solution bends light).
- Before fermentation, adding sugars to the solution increases both the relative density and the refractive index of that solution, allowing the refractometer reading to be translated (approximately) to a specific gravity reading.
- A Refractometer usually reads in Brix, which identifies the % Sucrose dissolved in water, while a hydrometer usually reads in Balling, Plato, or Specific Gravity. Balling, Brix, and Plato are for all intents and purposes identical, but Brix (as measured by a refractometer) is based on an interpretation of the refractive index assuming that the solution being measured is a Sucrose solution, while the others are expressions of the density of the solution. Because of this difference, the refractometer reading has to be corrected by applying a wort correction factor. The correction is made by dividing the reported Brix by the wort correction factor.
- Once the correction has been made, the reading can be converted to specific gravity using the formula [FONT="]SG = 1+ (Brix / (258.6 – ((Brix/258.2) *227.1))). There are other equations of greater or less complexity, but the quoted equation is used by Brewers Friend, and is accurate to 1 gravity point within the range of measurements used in brewing.[/FONT]
- [FONT="]To determine the appropriate wort correction factor see http://www.brewersfriend.com/how-to-determine-your-refractometers-wort-correction-factor/ You need to use a hydrometer and the refractometer to measure the SG and reported Brix, and enter them into the spreadsheet. Brewers Friend suggests that you take a refractometer reading 5 times for each sample of wort, and enter the average reading into the Brix field. If I do this, I get 5 identical refractometer readings, so I only take one reading.[/FONT]
- [FONT="]After performing a few batches (they recommend 6 batches), you get an average wort correction factor that you can enter into Brewer's Friends refractometer calculator without having to take any more hydrometer readings. The purpose of performing the calculations multiple times, is to eliminate measurement errors.[/FONT]
- [FONT="]A deviation of 0.01 in the wort correction factor causes a difference less than 1 gravity point for a 1.050 beer. When making a new recipe, I always recalculate the wort correction factor, and if it is different from the average by more that 0.01, I start a new spreadsheet for that recipe. This is because different grain bill combinations can require a different wort correction factor. The only instance I have found where this presents a problem is when using torrified wheat in a recipe, which reduces the wort correction factor by about 0.03.[/FONT]
All the above deals with using a refractometer and software to estimate the specific gravity prior to fermentation. Once fermentation starts however, things get a lot more complicated. The yeast consumes the sugars in the beer (which lowers the specific gravity), and produces alcohol as a by product. Is alcohol is less dense than water, the production of alcohol lowers the specific gravity even more. However, when using a refractometer, it does not measure specific gravity; it measures the refractive index. Reducing the amount of sugars (which lowers the refractive index) but alcohol has a higher refractive index than water (causing the refractive index to rise). Brewers Friend uses the Sean Terrill calculator for estimating the post fermentation gravity, but in my experience this produces some wildly inaccurate results. The problem is that most of the beers I make have high attenuation, and Sean Terrill himself admits that his calculator in inaccurate with highly attenuating beers. However, I do use my refractometer occasionally to detect when fermentation is complete. I simply take periodic Brix readings. When the Brix readings stop dropping, then fermentation is complete. If I need to know the actual FG, I take a single hydrometer reading.
Although this may seem complicated at first, it gets much easier as you get used to it. It is faster and wastes much less beer in samples, not to mention the broken hydrometers, or the effect on my blood pressure when the hydrometer settles with the scale facing in the wrong direction.
Hope this helps,
-a.