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# Understanding Specific Gravity vs. Plato

The simple hydrometer can tell us the gravity of our wort, and therefore the amount of extract we have recovered from our ingredients, and can even be used to tell us what extract we can expect from different malts. The hydrometer can also tell us how much extract the yeast has used during fermentation, and can give us a reasonable approximation for the alcohol content of our beer. After the thermometer, the hydrometer is perhaps the most important measuring instrument in the brewer’s arsenal, yet many of us give little thought as to what it actually measures. Homebrewers usually use a hydrometer to measure specific gravity (SG), whereas commercial brewers more often use it to determine degrees Plato (°P), except in Britain where SG is more common. So what’s the difference and why might one system be preferred over another?

#### Definitions

If we start at the beginning, a hydrometer is an instrument that can float in a liquid, and how far it sinks in a liquid is a measure of the density of that liquid. Hydrometers are weighted according to the density of the liquid to be measured, and the weights can be adjusted to measure the density of a whole range of liquids including oils and petroleum, battery acid, and a variety of sugar solutions including beer wort. Strictly speaking, the term “hydrometer” should only apply to aqueous (or water-based liquids), but let’s not get too pedantic here. Each hydrometer carries a scale that can be calibrated to read the density of the liquid in various units, notably in our case, SG and °P.

Specific gravity is defined as the ratio of the weight of a given volume of the test liquid at a given temperature to the weight of the same volume of water at that same temperature. SG is the ratio of the densities of the two liquids, but as a ratio has no units, it is simply given as a number, such as 1.060. But SG is defined by the temperature at which the hydrometer and its scale were calibrated. That temperature is most commonly 60 °F (15.6 °C) for brewing SG hydrometers; it is possible to correct for measurements made at a different temperature, but it is best to measure your SG as close to the calibration temperature as possible.

Degrees Plato simply measures the density of the wort as percent sucrose. In other words, when you have a wort reading 10 °P on a Plato hydrometer, this means that the wort has the same density as a 10% sucrosesolution at the same temperature. The temperature at which Plato instruments are calibrated is 68 °F
(20 °C) and, again, measurements should be made as close to that temperature as possible. Since it measures sugar concentration, an instrument reading in °P is more properly called a Saccharometer. Be very clear that the wort does not contain 10% sucrose, for brewing worts do not usually contain only sucrose but rather a mixture of sugars, such as glucose, maltose, maltotriose and so on.

#### A Little Bit of History

The concept of specific gravity was a not a new one when the idea of using a hydrometer to measure beer strength first became a practical reality. This was in the latter part of the 18th century, when an Englishman, John Baverstock, carried out experiments in his brewery and worked out a method to use the instrument to measure wort density. He didn’t publish his work until after John Richardson, another English brewer had already published a method for using the hydrometer to measure both wort and beer strengths in 1784-85. Richardson called his instrument a Saccharo-meter, and used a somewhat odd scale. He calibrated it in “pounds per barrel,” which meant the extra weight of an English beer barrel of 36 Imperial gallons (about 43 US gallons) of a wort or beer over that of a barrel of water. It may look as though he was measuring SG by the definition given earlier, but it is not because of the units used in the scale (in fact SG = [lb. per barrel/0.36] + 1000). English brewers took up the use of Richardson’s Saccharometer and “pounds per barrel” was the normal unit used there until well into the 20th century, when SG became the norm.

That was unfortunate because such a unit was obviously peculiar to English brewers and did not appeal to their German brethren. So a gentleman by the name of Karl Balling in 1843 introduced a scale based on the concentration of sucrose in solution, making the assumption that sucrose solutions would have the same density as those of other sugars (which is not exactly true, but near enough for us). Balling’s scale was later (in 1918) improved upon by Fritz Plato, and his name became attached to this instrument, although the differences incorporated by Plato are small and of no practical significance to brewers. The scale was rightly named after Balling for many years after Plato made his corrections, but nowadays it is Plato whose name is ascribed to this system of measurement.

#### Which is Best?

The Plato scale became popular among commercial brewers in this country, partly because Richardson’s pounds per barrel system was inappropriate in a country where the English barrel was not in use, and partly because of the high proportion of German brewers in this country from the middle of the 18th century onwards. An important reason why the Plato system is liked by commercial brewers is that since it measures the wort concentration as sugar, then it is regarded as a direct measurement of brewing extract. In contrast, an SG hydrometer, strictly speaking, does not measure extract as sugar or as any other substance since SG is a ratio without units and is just a number. SG is now widely used by homebrewers because much of the literature and the ingredients when homebrewing became popular in the late 1970s and 1980s came from England where use of SG in brewing was the norm.

It is important to understand that both SG and Plato hydrometers really measure the same thing, since they both depend primarily on the density of the wort. I have already mentioned that we have sugars other than sucrose in brewing worts, and that these other sugars do have slightly different densities from those of sucrose. In practice, those differences are small enough to be ignored. However, if there are solids other than sugars present in solution (and therefore increasing the density of the wort), a Plato hy-drometer would read those other solids as percent sucrose and as an increase in brewing extract. Correspondingly, those other solids would also result in an increase in SG as compared to a similar wort that did not contain such solids. In other words, both instruments are subject to the same error in terms of telling the brewer how much extract he has in his wort.

In short, there is really nothing fundamentally different between the two systems, and which you choose comes down to practical considerations. At BrüRm@BAR in New Haven, Connecticut we use °P, partly because our hydrometer contains a mercury thermometer and it directly reads corrections due to deviations from the calibration temperature. Such instruments are very easy to use but are relatively expensive. SG instruments are generally cheaper, and although some do carry a built-in thermometer they are not usually calibrated to give adjustments for different temperatures. A disadvantage with SG is the somewhat awkward form of the readings — 1.xxx, which means SG numbers cannot easily be used directly in calculations, such as for determining brewhouse efficiency or recipe formulation. Instead you have to work in terms of “gravity points.” That is, use only the significant numbers after the decimal point.

However, SG hydrometers do have an advantage in terms of ease of reading, in the sense that “1” (that is 1.001) on the scale is only about one-quarter of 1 °P. So if the length of the hydrometer stem is the same and the range covered is the same in each case you can read SG more precisely than you can read °P, simply because the graduation marks are farther apart. In fact, for homebrewers, this is not really of practical significance, especially if the temperature of the measurement is not suitably controlled. I use several different SG hydrometers at home — one for “regular” brews covering 1.000-1.070, one for stronger beers with a range of 1.060-1.0130, and one for checking finishing gravity ranging from 0.980 to 1.020.

#### Relation Between SG and °P

Although both instruments basically measure the density of the liquid, there is no fundamental relationship between the numbers they read, although approximate conversion formulae have been derived. One simple equation has been used to link SG at 60 °F (15.6 °C) and °P at 20 °C (68 °F):
°P = SG points/4

Note that this equation uses SG points as discussed earlier and more importantly that it is only an approximate relationship. This relation holds fairly well, in practical terms, for worts up to about SG 1.050, but gives inaccurate results for higher strength worts and should not be used for them. Obtaining a more accurate relationship is complicated by the fact that the instruments commonly used are calibrated at different temperatures. For instance, The American Society of Brewing Chemists have published quite complete tables comparing SG at 20 °C (68 °F) with °P measured at the same temperature, but that doesn’t help a great deal if you are using an SG instrument calibrated at 60 °F (16 °C). You can make corrections for SG measured at different temperatures, but once you start doing so you are increasing the level of error in the treatment and might just as well stick to the simple equation above.

Several more equations for relating SG and °P more accurately have been proposed, one of the simpler ones is:
°P = 259 – (259/SG)

Where SG (not SG points) is measured at 60 °F (16 °C). The results for this equation are illustrated in the graph below.

#### Conclusion

So I have indicated that SG and °P really measure the same thing but simply record the results in different ways. I have also shown that there is no great advantage in one system over the other, so whichever one you choose is entirely up to you. The most important thing is to be consistent and stick to the same system, since relationships between the two are clouded by the different calibration temperatures used for each type of instrument. The reason I have given two relatively simple ways of converting from SG to °P and vice versa is that this may be useful in deciphering recipes from another source, or if all your previous results are in one system and you have broken that hydrometer and have to use one working on the other system. Or, you may be in my position where I use only SG hydrometers in brewing at home, and only Plato instruments when brewing at BrüRm@BAR, so I need to know how to go from one system to another when converting recipes.

Issue: October 2014