For brewers it’s usually standard measures to take gravity readings of the wort prior to pitching, after fermentation is complete, and why not even during fermentation to monitor the progress of fermentation. This is of course done to measure the sugar contents of the wort, and will help the brewer approximate what kind of alcohol levels to expect in the finished beer, and to see whether there still remains sugar to ferment. What is actually happening when one is taking a gravity reading, is that one is measuring the density of the wort or beer. The density is then usually expressed in specific gravity (SG), which is the density of the wort corrected against (divided with) the density of water (0.9982071 g/ml at 20° C), or in degrees Plato, which compares the density of the wort with that of a sucrose solution with the same percentage of dissolved sucrose by weight (so a 10° Plato wort has the same density as a 10% (w/w) sucrose solution). The amount of dissolved sugar in the wort (g / 100g wort) is also called the extract of the wort, and it is usually expressed in degrees Plato.

There is not a linear relationship between degrees Plato and specific gravity, but a very simple approximation is (1):

A much better approximation is the one given by Lincoln (1987) (2):

If we test these out with a specific gravity of 1.048, the first equation gives 12° Plato, while the second gives 11.91° Plato. Close, but not exactly the same. The further from 1 we go, the less accurate the first equation will be. A specific gravity of 1.092 will give 23° Plato with the first equation, but 22° Plato with the second. Of course the second equation isn’t perfect either, and it will also give better approximations closer to one. Other approximations can be found in e.g. Siebert (1980).

So now we know we are actually measuring the density of the wort, and then using it to approximate the sugar content of the wort. This approximation is then expressed as Specific Gravity, degrees Plato, or whatever other unit you wish. But what happens with the density of the wort/beer after fermentation has produced ethanol out of the fermentable sugars? Ethanol has a density of 0.78945 g/ml at 20° C, quite much lower than water, and hence it will skew the scale. Take for example a 1.048 or ~12° Plato wort, containing no ethanol, and a 1.048 or ~12° Plato beer, with 12% ethanol (let’s say it’s a sweet and strong Imperial Stout). Will these to solutions contain the same amount of dissolved sugar? No! But, both have the same specific gravity you might argue? Yes, they do have the same specific gravity, but the 12% ethanol content of the beer will skew the measured gravity value, and the actual extract of the beer is much higher. This allows us to introduce two new terms, apparent extract and real extract. Apparent extract is the measured extract value (be it in specific gravity, degrees Plato or as density in g/ml), while real extract is the actual amount of dissolved sugars in the beer/wort. By simply measuring the density, it is impossible to estimate the real extract accurately. One should either know the original extract of the wort (i.e. the extract before fermentation began) and preferably the ethanol content as well. The real extract can of course be measured directly by the likes of liquid chromatography or similar, but is usually overkill, since the approximations are quite good.

By taking into account the lower density of ethanol, one can approximate the actual amount of sugars dissolved in beer, i.e. the real extract (from now on RE). One simple approximation used by many brewers is one derived from data by Karl Balling during the 19^{th} century (3):

This requires only a measurement of the apparent extract (in degrees Plato; from now on AE) and information on the original extract (in degrees Plato; from now on OE), which usually is measured prior to pitching. Another slightly more accurate approximation can also be made from assumption presented by Karl Balling (that for each 2.0665 g of carbohydrate consumed by the yeast, 1 g of ethanol is produced together with 0.11 g of biomass and 0.9565 g of carbon dioxide) (4):

This approximation requires information on the ethanol content by weight. The problem with these approximations is again that they are only accurate within a range of input values. Pawlowski & Doemens (1932) built upon these approximations by correcting them to various OE values. The following approximation can thus be used (5):

*q* is a coefficient dependent on the OE, and it can be obtained from the following table:

[table id=4 /]

If we want to get even more accurate, we can use the following response surface-type function proposed by Hackbarth (2009) which he derived from measured values (6):

This function is accurate within ±0.0015° P for *A*_{ABW} 0-7% and AE 0-10° Plato.

Let’s test out these functions on some actual fermentation data I measured during the week. The density of the wort prior to pitching was 1.059392 g/ml, equaling to a specific gravity of 1.061295. Converting to degrees Plato with Lincoln’s approximation (2) gives 15.04° Plato. This wort fermented down to a density of 1.01144 g/ml, equaling to a specific gravity of 1.013263. Converting this to degrees Plato with Lincoln’s approximation gives us an Apparent Extract of 3.38° Plato. The measured ethanol content was 6.39% ABV. We can convert this to ABW with the following equation using data from Weissler (1995) and the International Bureau of Legal Metrology (1975) (7):

Using this formula gives us an ABW of 4.99%. So what is the real extract? Using the different equations presented, we get the following values:

(3) 5.60° P

(4) 5.54° P

(5) 5.60° P (*q* = 0.235)

(6) 5.67° P

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.

**References:**

- Cutaia, A., Reid, A., Speers, R., Examination of the Relationships Between Original, Real and Apparent Extracts, and Alcohol in Pilot Plant and Commercially Produced Beers.
*Journal of the Institute of Brewing***115**(2009) 318-327 - Hackbarth, J., The effect of ethanol-sucrose interactions on specific gravity.
*Journal of the American Society of Brewing Chemists***67**(2009) 146-151 - International Bureau of Legal Metrology, 1975.
*International Alcoholometric Tables*, The Society: Partis - Lincoln, R., Computer compatible parametric equations for basic brewing computation.
*Master Brewers Association of the Americas Technical Quarterly***24**(1987) 129-132 - Pawlowski, R., Doemens, A., 1932.
*Die Brautechnischen Untersuchunds-Methoden*, Verlag von R: Oldenburg, Munich. - Siebert, K., Routine use of a programmable calculator for computing alcohol, real extract, original gravity and calories in beer.
*Journal of the American Society of Brewing Chemists***38**(1980) 27-33 - Weissler, H., 1995. Brewing calculations. In:
*Handbook of Brewing.*W. Hardwick Ed. Marcel Decker Inc: New York. pp 643-706