# Hydrometer & Refractometer Calculator

### Introduction

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:

All of the methods are designed to be used after fermentation, but they should be able to yield reasonable estimates of alcohol content during fermentation as long as there is enough alcohol to affect the measurements and the sample is degassed enough that the measurements are not affected by dissolved CO2.

### Input Field Definitions

Refractometer Reading – The refractometer reading for the wine after fermentation.  Range: 0° to 100°Brix

Hydrometer SG Reading – The hydrometer SG reading for the wine sample.  Range: 0.77193 to 1.55454

SG Reading Temperature – The temperature of the wine sample at the time of the SG reading.  Range: 0°C (32°F) to 40°C (104°F)

Calibration Temperature – The hydrometer calibration temperature of the hydrometer used to take SG reading.   Range: 0°C (32°F) to 40°C (104°F)

### Output Field Definitions

Corrected SG (20°C/20°C) – The temperature-corrected SG value.

Alcohol Content – The alcohol content of the wine calculated using the four calculation methods listed above.

True Brix – The total solids content of the wine calculated using the four calculation methods listed above.

### Calculation Details

The calculations involved in the four hydrometer and refractometer calculation methods are described in detail below.

#### Rogerson & Symington Method

Rogerson & Symington (2006) developed a method to estimate alcohol content and residual solids (true Brix) based on refractometer and hydrometer readings on 35 port wines. In the words of the authors, “It is not applicable for the analysis of dry wines, whether fortified or not, which contain insufficient soluble solids for Baumé determination by hydrometer, and is yet to be evaluated for sweet table wines, such as sauternes.”  However it is included in FermCalc because many home winemakers seem to find it useful for monitoring fermentation progress and calculating alcohol content.

FermCalc first converts the hydrometer reading sg to degrees Baumé using the following equation.

 Bé = 145 – 145/sg (5-17)

where is degrees Baumé.

Alcohol content is then calculated as:

 av = 1.646Ba – 2.703Bé – 1.794 (5-18)

where:

av = alcohol content, % by volume

Ba = refractometer Brix reading (apparent Brix)

True Brix, Bt, which represents the estimated residual solids content in % by weight, is then calculated as:

 Bt = Ba – 0.358av (5-19)

This method has a temperature basis of 20°C (68°F).

#### Son et al. Method

H. S. Son et al. (2009) developed the following six empirical equations based on refractometer, hydrometer, and alcohol content measurements on 30 wines before and during fermentation.

 Bt = -0.352Bi + 1.264Ba + 2.006 (5-20) Bt = 0.201Bi + 0.782Bh – 0.921 (5-21) av = 0.967Bi – 0.766Ba – 5.793 (5-22) av = 0.625Bi – 0.457Bh – 3.814 (5-23) Bt = 0.529Ba + 0.457Bh – 0.344 (5-24) av = 0.833Ba – 0.996Bh + 3.927 (5-25)

where:

av = alcohol content, % by volume

Ba = refractometer Brix reading (apparent Brix)

Bt = true Brix (% solids by weight)

Equations (5-24) and (5-25) allow calculation of alcohol content and true Brix directly from hydrometer and refractometer readings.  However, I found these equations to be inaccurate, yielding estimates of alcohol content that appear too high in the lower-alcohol range and too low in the upper range.  Instead of using equations (5-24) and (5-25), I developed alternative equations from equations (5-20) through (5-23) that appear much more accurate. Combining equations (5-22) and (5-23) to eliminate Bi gives:

 av = 1.400Ba – 1.292Bh + 0.197 (5-26)

Combining equations (5-20) and (5-21) to eliminate Bi gives:

 Bt = 0.459Ba + 0.498Bh + 0.143 (5-27)

Equations (5-26) and (5-27) are used by FermCalc to calculate alcohol content and true Brix.

This method has a temperature basis of 20°C (68°F).

#### Roesener Method

This method was published online by Werner Roesener (2001) and is very popular among home winemakers, but there is no documentation regarding the derivation of the equations.  My testing indicates that it yields results that are very similar to the other methods.

Simplifying the original equations we get:

 av = 1.5184Ba + 365(1.0 – sg) (5-28) s = 2520(sg – 1.0) + 3.1853av (5-29)

where s is the dissolved solids content in g/L. FermCalc converts the solids content in g/L to true Brix in percent by weight using equation (5-30) below.

 Bt = s/sg/10 (5-30)

This method has a temperature basis of 15.56°C (60°F).

#### Barth & Race Method

This method was originally developed by Georg Barth (1905) in Germany for analyzing beers. The original equations are:

 aw = 759.8(ri – 1.3330) – 292.3(sg – 1.0) (5-31) Bt = 336.6(ri – 1.3330) + 130.3(sg – 1.0) (5-32)

Where ri is the measured refractive index.  The equations were later modified by J. Race (1908) to yield more accurate results for beers with alcohol contents greater than 4.5% by weight.

 aw = 778(ri – 1.3330) – 290(sg – 1.0) (5-33) Bt = 350(ri – 1.3330) + 130(sg – 1.0) (5-34)

FermCalc uses equations (5-33) and (5-34) to calculate alcohol content and true Brix because they were intended for higher alcohol concentrations and might be more applicable for winemaking calculations.  The result of equation (5-33) is converted to % alcohol by volume as described here.

This method has a temperature basis of 15.56°C (60°F).