# Gravity/Density/Sugar Conversions

**Details:** Conversion between various units of density. Some conversions are not perfect, for example specific gravity and °Brix do not measure the same physical property, and are often measured using different instruments. Some of these conversion are therefore based on expressions derived from polynomial fits to experimental data sets.

**Potential alcohol** is not a measure of density, but it is useful. This calculation is an approximation, for more detailed alcohol prediction see the alcohol prediction calculator.

**Dissolved Sugar** is not a measure of density, but is useful. This is an estimate of dissolved solids assuming that most of the solids are sucrose - it will be close to the true value.

Every value is calculated from specific gravity. If another value, such as Baume is provided, it is first converted to specific gravity, and then all other values are calculated from that.

Calculating °Brix from SG is based on an expression from a polynomial fit to a large data set:

brix = 143.254 * sg^{3} - 648.670 * sg^{2} + 1125.805 * sg - 620.389

Potential alcohol is calculated as discussed in the alcohol predicition section, with the assumption of a final gravity of 1.000, and a correction for DSOS of 0.007.

Oechsle has a simple relationship with SG:

oechsle = 1000 * (sg - 1.0)

Baume is also a simple relationship:

ba = 145 - (145 / sg)

Babo/KMW is also a simple relationship:

KMW = baume * 1.53

Grams per litre is obviously simply:

gl = 1000 * sg

Grams per litre of dissolved solids is calculated from the specific gravity, and the °Brix. Subtly, these measure different things, the specific gravity tells us the density of the liquid (grams per litre) and the °Brix tells us the dissolved solids (percentage mass of solute to solution - grams per 100 grams). This allows us to calculate the dissolved solids, thus:

dissolved solids = gravity * (brix * 10)

The gravity tells us how much 1 litre of the liquid weighs (in kg) - we then multiply this by the dissolved solids ratio to give dissolved solids per litre. 'brix * 10' simply corrects the °Brix value from being grams per 100 grams to being grams per kg. Thus, we time number of kg in one litre, by the number of grams dissolved per kg, and are left with the number of grams per litre.

To get from any of those values back to specific gravity involves a rearrangement where possible. For °Brix to SG, another expression was generated by polynomial analysis:

sg = 0.00000005785037196 * brix^{3} + 0.00001261831344 * brix^{2} + 0.003873042366 * brix + 0.9999994636

Potential alcohol to sg is a complex rearrangment, it works out to be:

sg = (9221 * pa + 805600) / (3000 * pa + 800000)

**VinoCalc** by Jonathan Musther - jon@musther.net