The purpose of this article is to provide the basics of how to convert degrees Plato to specific gravity. Why would you want to? Many brewers use degrees Plato to describe a wort's percent extract by weight and many recipes will give the original gravity and final gravity in degrees Plato. So, if you want to use these recipes, you will need to convert the units, Plato to SG, and SG to Plato.
Brewers in the 1800's in Bohemia and Germany, wanted to come up with a way of measuring the amount of fermentables (ie. sugar) in their wort. Rather than just check the specific gravity, which measured the wort's total density, they wanted to correlate the density with the amount of sugar or fermentables in their beer. So, they carefully made solutions of sugar (in this case sucrose, because it would give the most weight per unit of water) and water, then weighed the known volume of this sucrose solution to determine their densities (in % sucrose extract by weight or Plato/Balling). In other words, to say your wort is 15 degrees Plato (or Balling), would mean that if your wort's fermentables were 100% sucrose they would make up 15% of the total weight. Although we know our wort is not made up of 100% sucrose, it doesn't really matter because we just wanted a way to measure the total fermentables that would give a consistent number time after time. Just like the specific gravity of wort is compared to the specific gravity of water, the water is just an arbitrary variable which always gives us the same values each time we measure against it (adjusted for temperature of course). Since we are using the hydrometer to measure degrees Plato and specific gravity, a correction factor must be applied for variations in temperature for both readings. The original idea for measuring the fermentables was presented by Karl Balling in 1843, but was improved upon by the German Fritz Plato. Both are so close that we can consider them identical.
Although degrees Plato was derived by actually measuring the weight of the sucrose solutions, others have come up with formulas which approximate the relationship between degrees Plato to specific gravity at 60 degrees F (15.5 degrees C).
The formulas are:
degrees P = SG points/4 (1.050 is "50 points"). A more accurate formula is: degrees P = 259-(259/SG) & SG=259/(259-degrees P).
There are more complicated formulas if you want to learn them for converting Plato to specific gravity. If you are interested, read the article in Brewing Techniques by Martin P. Manning Republished from Brewing Techniques' September/October 1993. But for the majority of homebrewers, these formulas will provide all the accuracy they need. Let's work through a few examples of converting degrees Plato to specific gravity: a recipe which gives the original extract as 15 degrees Plato would have an original gravity of OG = 259/(259-15) = 259/244 = 1.061. The apparent extract (Apparent Extract is the final gravity of the beer, converted to degrees Plato) is 3.4 degrees Plato, so the FG = 259/(259-3.4) = 1.0133. A quick and dirty rule of thumb is: the SG is 4 times the degrees Plato, so 15 degrees Plato x 4 = 60 gravity points (compared to 61 points) and 3.4 degrees Plato x 4 = 13.6 point compared to 13.3 points. It's close enough for most of us and much easier to remember.
This article was adapted from the article in Brewing Techniques Magazine written by Martin P. Manning and republished from Brewing Techniques' September/October 1993