Specific Gravity to Degrees Plato

Brewing measures the same quantity — dissolved extract in wort — on two scales that will not sit still next to each other. Specific gravity is the density of the wort divided by the density of water, so a wort at 1.048 is 4.8% denser than water. Degrees Plato is the percentage of extract BY WEIGHT: 12 °P means twelve grams of dissolved solids in every hundred grams of wort. One is a density ratio, the other is a mass fraction, and the relation between them is a curve rather than a factor.

The form used here, $P = 259 - 259/SG$, is a two-term approximation to that curve and it is accurate to a few hundredths of a degree across the whole range of real wort. The full relation is a cubic polynomial fitted to the Plato tables, which were themselves fitted from Balling's sucrose-solution densitometry in 1843 and refined by Plato's group at the Imperial Institute around 1900. Wort is not a sucrose solution, so even the tables are an approximation — a well-founded one, since maltose and sucrose happen to be close enough in density behaviour that the substitution costs less than the measurement error.

The convenient rule most brewers carry is that one degree Plato is about four gravity points, and it is a good rule between roughly 5 and 20 °P. It drifts at the extremes, because the true relation is not linear, and the drift always runs the same direction: the rule under-reads strong worts. Brix, which appears on every refractometer, is the same scale as Plato for practical purposes — both are percent sucrose by weight, calibrated by slightly different methods, and the difference between them is smaller than the error in reading either instrument.

The mistake worth naming is applying this conversion to fermented beer. Both scales assume the only thing dissolved in the water is sugar. Once ethanol is present the assumption collapses, because ethanol is substantially LIGHTER than water and pulls the density down while contributing nothing to the extract. A finished beer reading 1.010 does not contain 2.6 °P of sugar; it contains rather more, disguised by the alcohol. That gap is exactly why brewers distinguish apparent extract from real extract, and it is why a refractometer reading taken during fermentation needs a correction before it means anything at all.