### Introduction

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:

The calculator will adjust the hydrometer readings for temperature if the measurement temperatures and the hydrometer calibration temperatures are provided. If the entered SG values are already corrected for temperature, or if temperature corrections are not desired, simply enter 20°C (68°F) in all of the temperature fields and no corrections will be made.

This calculation is only valid for SG or density measurements obtained with a hydrometer or some other device for directly measuring SG or density. It does not work with refractometer readings because of the obscuration effect of alcohol on refractive index. The final SG measurement must be taken prior to any post-fermentation sweetening. If any sweetener is added during fermentation after the initial SG measurement is taken, the initial SG measurement must be adjusted accordingly.

Dr. William Honneyman (1966) compared alcohol levels calculated using the SG drop method to the distillation data of Thorpe & Brown (1914) and found that it gives results “reasonably comparable with tests by distillation, provided graded factors suited to each drop in gravity are used”. While he did not recommend a specific way to calculate the graded factors, he provided an important validation of the approach in general.

### Input Field Definitions

Hydrometer SG Reading – The initial and final hydrometer SG readings. The initial reading should be taken prior to fermentation, and the final SG reading should be taken after fermentation is complete. Range: 0.77193 to 1.55454

SG Reading Temperature – The temperatures of the must and wine samples at the time of the initial and final SG readings. Range: 0°C (32°F) to 40°C (104°F)

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

### Output Field Definitions

Corrected SG (20°C/20°C) – The temperature-corrected initial and final SG values.

Alcohol Content – The alcohol content of the wine calculated from the difference between the initial and final corrected SG values using the four calculation methods listed above.

True Brix (Solids Content) – The total solids content of the wine calculated from the final corrected SG value and the average alcohol content of the four calculation methods.

### Calculation Details

The calculations involved in the four hydrometer SG drop calculation methods are described in detail below.

#### Berry Method

This is the most commonly used SG drop method, and is described on pages 79-80 of *First Steps in Winemaking* by C. J. J. Berry (1987). It estimates the alcohol content by dividing the drop in SG by the constant 0.00736, or:

a = (_{v}sg – _{i}sg) / 0.00736_{f} |
(5-8) |

where:

*a _{v}* = alcohol content, % by volume

*sg _{i}* = initial SG

*sg _{f}* = final SG

Ritchie Products Co. (2004) claims to have compared the results of equation (5-8) to the results of gas chromatography for a wide range of wines, and found that the results were within 0.3% vol/vol.

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

#### Duncan & Acton Method

This method is described on pages 64-66 of *Progressive Winemaking* by Peter Duncan and Bryan Acton (1967). The Duncan & Acton method calculates the alcohol content from the initial and final specific gravities divided by a factor *F* that is a function of the corrected initial SG. The equations are as follows.

a = 1000(_{v}sg – _{i}sg) /_{f} F |
(5-9) |

F = 7.75 – 3000(sg – 1.0) / 800_{c} |
(5-10) |

sg = _{c}sg – 0.007_{i} |
(5-11) |

where:

*a _{v}* = alcohol content, % by volume

*sg _{i}* = initial SG

*sg _{f}* = final SG

*F* = conversion factor

*sg _{c}* = initial SG corrected for non-sugar solutes

Combining equations (5-9) through (5-11) above yields the following equation:

a = 1000(_{v}sg – _{i}sg) / [7.75 – 3.75(_{f}sg – 1.007)]_{i} |
(5-12) |

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

#### Balling Method

The Balling method is normally used for beer but gives results that agree very well with the other methods. The equations used in FermCalc were taken from Michael Hall’s article “Brew by the Numbers” in the Summer 1995 issue of *Zymurgy* magazine. In the original equations, specific gravities are expressed as degrees Plato, which FermCalc treats as being the equivalent as degrees Brix. The method requires the calculation of a parameter called “Real Extract”, which is an estimate of the residual solids content after fermentation has finished, as follows:

q = 0.22 + 0.001B_{i} |
(5-13) |

RE = (q·B + _{i}B) / (1 + _{f}q) |
(5-14) |

where:

*q* = attenuation coefficient

*RE* = real extract

*B _{i}* = initial Brix

*B _{f}* = final Brix

The alcohol content (% by weight) is then calculated as:

a = (_{w}B – _{i}RE) / (2.0665 – 0.010665B)_{i} |
(5-15) |

where *a _{w}* is the alcohol content in % by weight.

The result of equation (5-15) is then converted to % alcohol by volume as described here.

This method has a temperature basis of 17.5°C (63.5°F).

#### Cutaia, Reid, & Speers Method

Cutaia, Reid & Spears (2009) analyzed data from 532 beers to develop equation (5-16) below relating alcohol content to the initial and final specific gravities.

a = (_{w}B – _{i}B)(0.372 + 0.00357_{f}B)_{i} |
(5-16) |

The alcohol content of the beers ranged from 3% to 7% by weight (approx. 3.8% to 8.7% by vol.). As with the Balling equation above, the specific gravities for the analyzed beers were expressed in degrees Plato, which is assumed by FermCalc to be the same as degrees Brix.

The result of equation (5-16) is then converted to % alcohol by volume as described here.

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

#### Estimation of Solids Content (True Brix)

After we know the alcohol content, we can estimate true Brix, which represents solids content in % by weight, by using the model developed by James Hackbarth (2011), which is described here. This is done by treating the specific gravity *SG* and alcohol content *A* as known values and iteratively solving equations (5-38) through (5-44) for the true Brix *E*. FermCalc uses the alcohol content calculated by the Duncan & Acton method for this calculation.