beer alcohol measurement

I bought an alcohol hydrometer (scale $0-40\%$) to measure the alcohol in my home made beer, at the end of fermentation and prior to bottling. While it is accurate on pure water (@ $0\%$), home made wine (@ $8\%$), and gin (@ $40\%$), it will not work for beer. I've even tried it on a canned beer of 5% and then it shows a negative figure of -3. I've done all testing @ $\pu{20 ^\circ C}$ and cleared the gas from the liquid. If anybody got any ideas for this misreading, please let me educated. 




I think you are using hydrometer, which has a scale to measure alcohol percentage of the distillate. It should also has a scale to measure specific gravity of your fermentation mixture. I think what you have been doing wrong is you are using the scale to measure alcohol percentage to measure in your fermentation mixture. 


This gives you the measure of fermentation mixture’s density as compared to water (if you have used the scale of specific gravity). Sugar increases density, so by measuring the gravity of your beer mixture, you can know how much sugar it contains. By taking one reading at the beginning of fermentation (only contain sugar, yeast, and water) and another at the end of it (any amount of remaining unconverted sugar, yeast, alcohol produced, and water), we can calculate how much sugar has been converted into alcohol, and therefore, the alcohol content of the beer. The density at the beginning should be greater than the final density, because sugar (more dense than water) converted to ethanol (less denser than water). According to [Brewer's Friend - ABV-Calculator](https://www.brewersfriend.com/abv-calculator/):


$$ABV(\%) \approx (\text{Initial Gravity} - \text{Final Gravity}) \times 131.25 \tag{1}$$


Thus, if your initial gravity was 1.108, and your final gravity was 1.043, the equation $(1)$ your beer is approximately 8.79% alcohol by volume.


$$ABV(\%) \text{ of your beer} \approx (1.108 - 1.043) \times 131.25 \approx 8.53\%$$


(**Note:** $ABV$ stands for alcohol by volume).


**Few needs to know facts:**


1. Hydrometers are calculated to different temperatures, usually $\pu{60 ^\circ F}$ or $\pu{68 ^\circ F}$. There should be an instruction sheet comes with your hydrometer. Check the temperature of your beer mixture (wort), before you take density reading. Then use the temperature calibration instructions in the chart sheet for how to adjust the gravity if needed (Remember, gravity change with temperature; liquid expands).
2. As mentioned above, most hydrometers have a few different units of measurements printed on them; you are looking for the gravity reading for this purpose (reading will be a number within $1.000 - 1.160$ or beyond.
3. Some hydrometers can be used for wine and other liquid, as well (these hydrometers will come with a reading called the *Brix Scale*, to calculate $ABV$, or you can use [Brewer's Friend - Brix Converter](https://www.brewersfriend.com/brix-converter/)).


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