On the relationship between Plato and specific gravity

One of the most important measurements in brewing is the “sugar” content of wort and, later, beer. Sugar is in parenthesis because what is dissolved in wort is more than just sugar. It’s various sugars, proteins, lipids, minerals and trace elements. The professional brewing world refers to this collection of compounds as extract.

There is a strong and very predictable relationship between extract content of wort and its specific gravity. Because of this relationship we brewers can use hydrometers to measure wort extract content. Around the 1900s Karl Balling, Adolf Brix and then Friz Plato established a correlation between the density (specific gravity) and the sugar content of pure sugar. Each measured with more precision that the predecessor.

To make high precision specific gravity measurements, a device called the pyknometer is used. The volume of liquid held in a pyknometer is known at a very high precision and by weighing it empty and with the liquid to be tested, the density of the liquid can be determine very accurately.

The results of these measurements are available in tables in which the density for various sugar concentrations, expressed as weight percentage of sugar, is given. This relationship is only true for a given standard temperature. These sugar weight percentages are also referred to as degree Balling, degree Brix or degree Plato (°P). Essentially they are all the same. Degree Balling is rarely used anymore, degree Brix has been adopted by the wine industry (hence its use in refractometers) and Plato is used by the brewing industry.

Brewers, especially home brewers, commonly use specific gravity (1.xxx) or gravity points to express extract content without first converting to Plato. This is possible since the relationship between sugar content and specific gravity is reasonably linear. It’s also worth noting that the mix of compounds dissolved in wort doesn’t change the specific gravity exactly as pure sugar does. But this is ignored by convention. I.e. a wort with specific gravity X is assumed to have the same extract content as a pure sugar solution with the same specific gravity. In practice there is not much of a difference anyway.

To convert specific gravity to degree Plato the ASBC (American Society of Brewing Chemists) published a polynom that fits the data published in Plato’s tables (1):

A quick and dirty conversion between specific gravity and Plato is Plato = gravity points / 4. This formula works well up to a specific gravity of 1.060 where the error approaches 2%.

The relationship between specific gravity (density) and extract content (Plato) can also be used to calculate the volume increase caused by the dissolved extract. Many brewers don’t know that the volume of wort they produce is actually larger than the volume of water that is added. This is because the sugar increases the total volume of the solution.

Let’s assume 1 liter of water and dissolve 150 g of extract. The resulting wort has 0.15 / (1.00 + 0.15) = 13.04 Plato since Plato is the extract weight as percentage of the combined extract and water weight. A 13.04 Plato wort has a density (specific gravity) of 1.0527. Thus the 1.15 kg wort has a volume of 1.15 / 1.0527 = 1.092 l. This is 0.092 l more than the initial water. In general, each kg of dissolved extract increased the volume by about 0.61 l (0.3 qt for each pound)

This volume increase doesn’t matter much for general brewing calculations. When calculating the amount of water needed this effect leads to lower than actual grain absorption. A case where it does matter is calculating the efficiency of no-sparge or batch sparge lauter efficiency since that is determined by the ratio of the volume collected in the kettle over total volume in the mash.

Most tools, including Brewer’s Friend roll the volume increase from the sugar into the grain absorption factor (so even though it is happening, you don’t have to worry about it).

(1) A.J. DeLange: Specific Gravity Measurement Methods and Applications in Brewing

The following image shows the same hydrometer with the SG (specific gravity) and Brix/Plato scales:

For more articles on the subject of hydrometers:

Hydrometers readings are temperature dependent. All hydrometers are calibrated to a certain temperature – typically (59° F / 15° C) or (68° F / 20° C).  Use this calculator to adjust:
https://www.brewersfriend.com/hydrometer-temp/

Hydrometers are sometimes incorrectly calibrated at the factory, see our article on how to test yours:
https://www.brewersfriend.com/2010/12/19/instrument-calibration-for-maximum-brewing-awesomeness/

Post by Kaiser

Brewer’s Friend would like to welcome Kai of Braukaiser.com as a guest blogger and technical advisor! We’d also like to say thank you to him for his recent input on our October 2012 release, which included Plato support!