# Alcohol & Solids Content Calculators

### Calculator Descriptions

FermCalc includes six calculators related to alcohol and solids content estimation:

1. Hydrometer SG Drop – The Hydrometer SG Drop Calculator estimates the alcohol content of a wine from two specific gravity (SG) measurements: one obtained prior to fermentation, and one obtained after fermentation is complete.  Four different calculation methods are used to estimate alcohol content:
• Berry
• Duncan & Acton
• Balling
• Cutaia, Reid, & Speers
1. Hydrometer & Refractometer – The Hydrometer and Refractometer Calculator estimates the alcohol content of a finished wine from a refractometer reading and a hydrometer specific gravity (SG) reading.  Four different calculation methods are used to estimate alcohol content:
• Rogerson & Symington
• Son et al.
• Roesener
• Barth & Race
1. Boiling (Spirit Indication) – The Boiling (Spirit Indication) Calculator estimates the alcohol content of a wine from two specific gravity (SG) measurements: one obtained on a sample of the finished wine, and one obtained on a sample of the wine in which the alcohol has been boiled off and distilled water has been added to restore it to its pre-boiled volume.  Four different calculation methods are used to estimate alcohol content:
• Tabarié (Division)
• Blunt (Subtraction)
• Honneyman
• Hackbarth
1. Potential Alcohol – The Potential Alcohol Calculator estimates the alcohol content of a wine that will result from the complete fermentation of a must with a given initial specific gravity.  Nine methods are used to estimate the potential alcohol content:
• Dubrunfaut
• Marsh
• Margalit
• Cooke & Lapsley
• CEC Method
• Pambianchi
• Duncan & Acton
• Honneyman
• User Defined
1. OIML Calculator – The OIML Calculator solves the general formula for calculating the densities of mixtures of ethanol and water found in International Recommendation 22: International Alcoholometric Tables by the International Organisation of Legal Metrology (OIML, 1973).
1. Dry Matter – The Dry Matter Calculator determines the solids content of a wine from its alcohol content and specific gravity.  This is useful for winemakers who determine the alcohol content of their wines by other means, such as distillation or ebulliometry, and would like to calculate solids content.  Two methods are used to determine the solids content:
• OIV
• Hackbarth

Calculation details for each of the calculators are described in detail on the individual calculator pages linked above.

### Hydrometer Temperature Corrections

FermCalc allows hydrometer readings to be corrected for temperature in all of the alcohol content calculation methods except for the Potential Alcohol calculator.  The corrections are functions of both the alcohol and solids content of the liquids.  The alcohol correction is determined from the OIML formula (OIML, 1973).  The solids correction is determined from a fit of tables published in the AOAC Official Methods of Analysis (Williams, 1984) for correcting hydrometer btix readings.  These tables have a reference temperature of 20°C, so first the readings need to be corrected for the hydrometer calibration temperature if it’s different from 20°C.

The SG measured with a hydrometer is the ratio of the density of the liquid divided by the density of water at the hydrometer calibration temperature, or:

 sgaTc = ρT/ρwTc (5-1)

where:

sgaTc = apparent SG measured with a hydrometer with calibration temperature Tc

ρT = liquid density at temperature T, kg/L

ρwTc = water density at temperature Tc, kg/L

To correct the reading to a reference temperature of 20°C, we simply need to multiply the hydrometer reading by the ratio of the water density at the old calibration temperature to the water density at 20°C, or:

 sga20 = sgTc (ρwTc/ρw20) (5-2)

where:

sga20 = apparent SG corrected to a reference temperature of 20°C

ρw20 = water density at 20°C, kg/L

Water densities are calculated using the OIML formula assuming 0% alcohol.

After correcting for the hydrometer calibration temperature, we can correct for the sample temperature.  The coefficient of thermal expansion for aqueous ethanol-sucrose solutions, which determines the change in density for a given change in temperature, depends on both the ethanol and sucrose levels, but mainly on the ethanol level (Espejo and Armada, 2011).  To correct the measured SG, FermCalc determines a composite correction factor by first calculating three density correction factors as follows:

 dw = ρw20 / ρwT (5-3) da = ρa20 / ρaT (5-4) ds = ρs20 / ρsT (5-5)

where:

dw = density correction factor for pure water

da = density correction factor an ethanol-water solution with the same alcohol content as the liquid

ds = density correction factor a sucrose-water solution with the same sucrose content as the liquid

ρw20 = water density at 20°C, kg/L

ρa20 = ethanol-water solution density at 20°C, kg/L

ρs20 = sucrose-water solution density at 20°C, kg/L

ρwT = water density at the measurement temperature, kg/L

ρaT = ethanol-water solution density at the measurement temperature, kg/L

ρsT = sucrose-water solution density at the measurement temperature, kg/L

The corrected SG sgc20 is then calculated as:

The densites for water and ethanol-water solutions are based on the OIML formula.  The change in density of sucrose-water solutions with temperature is based on the following curve fit of the AOAC brix correction tables:

 B = Ba + [a(T – 20)2 + b(T – 20)] (5-7)

where:

B = corrected Brix

Ba = apparent Brix at temperature T

T = measurement temperature, °C

a = 1.4525·10-7Ba2 – 2.5256·10-5Ba + 1.2495·10-3

b = -6.6927·10-6Ba2 + 9.6012·10-4Ba + 4.4174·10-2

The plot below compares the AOAC data with the calculated Brix corrections from equation (7) above.

The temperature corrections are valid in the temperature range from 0°C to 40°C, which is the overlapping range of validity between the OIML formula and the AOAC tables.  Some of the alcohol content calculation methods below are based on SG values at 60°F instead of 20°C, in which cases the appropriate densities are substituted into the above equations.  FermCalc only reports the SG values corrected to 20°C, so the actual SG values being used in the equations will be slightly different than the reported SG values in these cases.