# Calculator

**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)

**Details:** A simple conversion between °F and °C and visa versa.

Simple linear relationship:

F = C * (9 / 5) + 32

C = (F - 32) * (5 / 9)

**Details:** This calcaultor converts between commonly used volume measurements.

Simple linear relationships:

US gallons = litres * 0.2642

Gallons = litres * 0.22

**Details:** This calcaultor converts between commonly used mass measurements.

Simple linear relationships:

Tonnes = kilograms / 1000

Tons = kilograms * 0.0009842

Pounds = kilograms * 2.205

**Details:** This calcaultor converts between the commonly used measurements of vineyard area.

1 hectare (or square hectometre) = 10,000 square metres (a square 100m by 100m)

Simple linear relationship:

Acre = hectare * 2.4710538

Note that this is an international acre, a US survey acre is slightly different, with a conversion factor of 2.4710439.

**Details:** This calculation corrects the ebulliometer reading based on the calibration reading, and then calculates the alcohol content.

Initially, the ebulliometer degree is calculated:

ebulliometer degree = calibration - reading

This essentially yields the number of degrees below the boiling point of water, at which the sample is boiling.

Next, a polynomial expression generated from a large data set is used to give the alcohol (% by volume):

alcohol = 0.0002590805845 * d^{4} - 0.0006404605357 * d^{3} + 0.001926392743 * d^{2} + 1.364664067 * d - 1.29216576

Where d = the ebulliometer degree.

**DSOS = **Dissolved Solids Other than Sugar

**Details:** This calculation is based on the method proposed by Duncan and Acton (*Progressive Winemaking*). The calculation is based on the initial and final gravity. The correction for DSOS is the the assumed gravity contribution from Dissolved Solids Other than Sugar. The correction for DSOS is hard to judge, but a suggestion is to use pre-ferment figures from wines for which you know the final alcohol, and tweak the DSOS until the calculation gives the correct value, then use the calculator for making predictions for similar musts (variety, region, condition etc).

This method of alcohol prediction is based on the method proposed by Duncan and Acton in Progressive Winemaking, the formula used is:

pa = 1000 * ((sg - dsos) - estsg) / (7.75 - 3000 * ((sg - dsos) - 1.0) / 800)

Where:

dsos = Correction for Dissolved Solids Other than Sugar

sg = measured specific gravity

estsg = estimated finishing gravity

**Details:** This calculator will calculate alcohol by volume from the spirit indication procedure. This procedure involves taking a sample of known volume and making a hydrometer reading. The sample is then boiled until it is reduced to about half its initial volume, topped up to the initial volume again with distilled water (or any water giving a hydrometer reading of 0.000), and a final reading is taken.

This calculator includes hydrometer temperature correction so it is not essential to ensure the initial and final readings are made at the same temperature, however the temperatures, and calibration temperature of the hydrometer must be known.

**Note:** This procedure, if performed carefully, will provide accurate results in wines regardless of residual sugar.

This calculator uses the same logic as in the 'Hydrometer Temperature Correction' calculator for correcting the readings for the temperatures at which they were taken. The difference between the initial and final gravities is then used to calculate the alcohol using the following formula:

alc = 0.008032927443 * si^{2} + 0.6398537044 * si - 0.001184667159

Where:

si = spirit indication (the difference between the gravities * 1000)

**Details:** This calculator uses a refractometer and hydrometer reading to ascertain the alcohol content of the sample. The gravity measurement must be from a hydrometer, and the °Brix measurement must be from a refractometer, these values must not have been calculated from one source.

Alcohol (ethanol) has a higher refractive index than water, so a dry wine will usually give a refractometer reading in the range 5 to 15°Brix.

This calculation uses the following formula:

alcohol by vol = 1.646 * b - 2.703 * (145 - 145 / s) - 1.794

Where:

b = °Brix reading (from refractometer)

s = specific gravity (from hydrometer)

**Details:** Monitor the progress of a ferment without having to take large samples and use a hydrometer, simply take a small refractometer sample. Entering the initial °Brix reading (pre-ferment) and the current reading will give is all that is required.

**Important:** There are a lot of approximations involved in this calculator. While this method is extremely useful for monitoring ferments, and on the whole quite accurate, it is not perfect - for example, do not expect it to show a true °Brix of exactly zero when the fermentation has finished.

A set of calculations are performed, first to calculate the initial gravity from the inital brix:

ig = 1.000898 + 0.003859118 * ib + 0.00001370735 * ib^{2} + 0.00000003742517 * ib^{3}

And then to calculate the current gravity from the initial and current brix:

cg = 1.001843 - 0.002318474 *ib - 0.000007775 *ib^{2} - 0.000000034 * ib^{3} + 0.00574 *cb + 0.00003344 * cb^{2} + 0.000000086 *cb^{3}

The alcohol by volume is calculated thus:

abv = 0.93 * ( ( 1017.5596 - ( 277.4 * cg ) + ( 1.33302 + 0.001427193 * cb + 0.000005791157 * cb^{2} ) * ( ( 937.8135 * ( 1.33302 + 0.001427193 * cb + 0.000005791157 * cb^{2} ) ) - 1805.1228 ) ) * ( cg / 0.794 ) )

Where:

abv = alcohol by volume

cg = current specific gravity

cb = current Brix reading (refractometer)

**NOTE** The 0.93 conversion factor was added based on experimental results to make the alcohol prediction for this particular calculator more accurate.

The residual sugar (in grams per litre) is calculated thus:

residual sugar = specific gravity * true brix

Spirit indication is calculated form the current alcohol thus, and used to adjust the current gravity, so that true Brix and residual sugar can be established:

si = (2 * SQRT ( 626159497 ) * SQRT ( 35209254016727200 * abv + 448667639342033000 ) - 33520822512398 ) / 841662180975

This is then used to calculate the corrected SG:

corrected_sg = current_sg - ( 1 - ( spirit_indication / 1000) ) + 1

Note that this alcohol calculation is different than the one used in the alcohol by refractometer and hydrometer as it gives more reliable results when coupled with the other calculations used to monitor fermentation using a refractometer.

**Details:** This calculator allows you to correct for the obscuration effect of the alcohol produced during fermentation, and calculate a true sugar concentration.

This calculator uses an assumption of the efficiency of alcohol production to calculate the 'true' Brix from the fall in Brix observed with a hydrometer. The derrived formula is:

True-Brix = ( 97 * i + 1200 * h ) / 1297

Where:

i = initial Brix h = current Brix (from hydrometer)

The above formula is derrived from the more easily understood:

Hydrometer reading = ( Brix_initial - Brix_current_true ) / 1.8

**Details:** A sample of high sugar juice can be diluted in order that it can be read on equipment with a limited scale. However because the °Brix scale is calibrated as %_{w/w}, but the dilution is carried out by measuring volume, the reading cannot simply be multiplied by the dilution to obtain the °Brix of the juice. This calculator corrects for this, allowing such dilutions to be used.

**Note on SG:** If measuring a juice using SG (specific gravity), simple multiplication is possible. For example, a sample diluted to 50% with distilled water, which reads 1.090, has a gravity of 1.180.

The calculations involved in this calculator are the same as those used in the gravity/density/sugar conversions. First the measured °Brix is used to calculate the gravity, which is then combined with the °Brix to calculate the dissolved solids. The dissolved solids is multiplied by (100/d), where d is the dilution percentage. So a dilution of 50% would mean multiplying the dissolved solids by 2. This number is then converted back to °Brix.

**Details:** The density of water changes predictably with temperature and so it is possible (and important) to correct readings taken at temperatures the hydrometer is not calibrated for. Most hydrometers are calibrated to 20°C, but some are calibrated to 15°C - any good hydrometer will have the calibration temperature marked.

This calculator, when working with a hydrometer calibrated to 20°C, is accurate over the approximate range 0-60°C, and when calibrated to 15°C, approximately 0-55°C.

The hydrometer temperatre correction for SG is performed with this expression:

corrected-reading = r * ((1.00130346 - (0.000134722124 * t) + (0.00000204052596 * t^{2}) - (0.00000000232820948 * t^{3})) / (1.00130346 - (0.000134722124 * c) + (0.00000204052596 * c^{2}) - (0.00000000232820948 * c^{3})))

Where:

r = reading

c = calibration temperature

This expression is based on °F, so the temperatures are first converted.

For °Brix, the expression used is:

correction = 0.0000006907947565 * temp^{4} + 0.0000008650898228 * temp^{3} * apb + 0.0000002111610273 * temp^{2} * apb^{2} - 0.000000420289855 * temp * apb^{3} + 0.0000000000000000003388131789 * temp^{4} - 0.00002646880494 * temp^{3} - 0.00003812273795 * temp^{2} * apb + 0.00002132555958 * temp * apb^{2} + 0.0000003140096619 * apb^{3} + 0.001470413886 * temp^{2} + 0.0003854292164 * temp * apb - 0.00001254869767 * apb^{2} + 0.04799327348 * temp + 0.0002013056055 * apb - 0.002157758291

Where:

correction = is the correction factor, added to the observed °Brix

temp = is the temperature difference from calibration (that is, reading temperature - calibration temperature)

apb = is the apparent °Brix, as read on the hydrometer

**Details:** This is a simple calculation of SO_{2} for the aspiration/oxidation method. Whether free, bound or total SO_{2} is calculated depends on the method you used.

**Red Wines:** Much of the 'free' SO_{2} in red wines is actually pigment (anthocyanin) bound - actual free SO_{2} levels will be very significantly lower.

The following formula is used:

SO_{2} = ( t * m * 1.6 * 1000 * 20) / v

Where:

m = molarity of NaOH

t = titre of NaOH required (mL)

v = volume of sample used (mL)

**Details:** This calculator will calculate the level of molecular SO_{2} in a wine based on its pH and measured free SO_{2} (the proportion of the measured free SO_{2} which is in the molecular form is dependant on pH). The required level of molecular SO_{2} for antimicrobial protection is often given as 0.8mg/L, although sometimes up to 1.5mg/L (Wine Science - Ronald S. Jackson - 2008).

**Red Wines:** In red wines, most of the 'free' SO_{2} is actually pigment (anthocyanin) bound, and is released by acidification of the sample prior to measurement. Due to this, it is not currently possible to ascertain the level of molecular SO_{2} in red wines. Red wines are however, generally far more microbially stable than whites, and thus are typically maintained at lower levels of 'free' SO_{2}. In summary, maintaining high molecular SO_{2} in red wines is difficult and ill advised - do not use this calculator as a guide for red wines.

The following formula is used to calculate the molecular SO_{2} from the free SO_{2} and the wine pH:

Molecular SO_{2} = FSO_{2} / ( 1 + 10^{( pH - 1.81 )} )

Where:

FSO_{2} = Free SO_{2}

pH = pH of the wine sample

The formula is then rearranged to calculate the required level of free SO_{2} to achieve a desired level of molecular SO_{2}:

Free SO_{2} = MSO_{2} * ( 1 + 10^{( pH - 1.81 )} )

Where:

MSO_{2} = Molecular SO_{2}

pH = pH of the wine sample

**Details:** This is a simple calculation of TA from a titration with NaOH.

The following formula is used:

ta = ( t * m * 75 ) / v

Where:

m = molarity of NaOH

t = titre of NaOH required (mL)

v = volume of sample used (mL)

**Details:** This calculation is based on the alcohol calculation from refractometer and hydrometer readings. The alcohol is calculated and then used together with the specific gravity to calculate the dissolved solids. The gravity measurement must be from a hydrometer, and the °Brix measurement must be from a refractometer, these values must not have been calculated from one source.

Alcohol has a higher refractive index than water, so a dry wine will give a refractometer reading in the range 5 to 10°Brix.

Initially the alcohol is calculated in the same way as for the 'Alcohol from Hydrometer & Refractometer', and then the following formula is used to calculate the dissolved solids:

ds = ( ( s * 1000 ) - 1000 + a * 1.264 ) * 2.52

Where:

s = specific gravity

a = alcohol, percent by volume

**Details:** This calculation is for simple deacidification using different agents:

Calcium carbonate - CaCO_{3}

Potassium carbonate - K_{2}CO_{3}

Potassium bicarbonate - KHCO_{3}

**Note:** Potassium salts are known to cause greater deacidification than this calculation predicts due to the potassium ions driving formation of potassium bitartrate. While this effect is small, it can be significant, and cannot be reliably predicted. Full realisation of the potassium bitartrate related component of deacidification may take some considerable time.

**Tip:** If you are treating a small volume, enter 1000 times the volume you have and the output will be in grams. For example, to deacidify 15 litres, type 15000 and the mass output will be in grams.

Simple deacidification is straight forward to calculate. Firstly, the difference between the current TA and the target TA is obtained, giving us the number of grams per litre we need to remove, this is then multiplied by the number of litres, to give the total number of grams of tartaric acid to remove.

As the deacidification agents used here react with tartaric acid in a 1:1 stoichiometric ratio, the factor to convert between grams of tartaric acid and grams of neutralising agent can be found by dividing the molecular mass of the agent by the molecular mass of tartaric acid. Thus, the overall formula is:

mass of agent (g) = ( ( current TA - Target TA ) * vol ) * (Mr agent / Mr tartaric acid)

Where:

Mr = molecular mass

150.087 = Mr of tartaric acid

100.087 = Mr of calcium carbonate

138.2055 = Mr of potassium carbonate

100.11 = Mr of potassium bicarbonate

**Details:** This calculator calculates the volume of wine to treat, and the mass of calcium carbonate (CaCO_{3}) required to treat it for double salt deacidification.

* The minimum volume to treat is the technically smallest volume of wine which needs to be completely deacidified. Allowing slightly more wine than this is the normal practice, as it ensures that the required deacidification is completed. The recommended volume to treat is simply 5% greater than the minimum, and is roughly in accordance with the volumes provided by the makers of Acidex®.

** Calcium carbonate (CaCO_{3}) is the deacidification agent. Brand name agents such as Acidex® consist almost entirely of calcium carbonate, but are seeded with crystals of the double salt, calcium malate-tartrate, designed to encourage precipitation of this salt. The mass calculated here can be used in either case.

**Tip:** If you are treating a small volume, enter 1000 times the volume you have and the output will be in grams. For example, to deacidify 15 litres, type 15000 and the mass output will be in grams.

Double salt deacidification is somewhat more complex than simple deacidification. A portion of juice is removed and completely deacidified, that is, unlike with simple deacidification, tartaric **and** malic acid are removed. This portion is then blended back to the bulk of the wine to have the desired effect.

The volume to treat is calculated with the following formula:

volume (L) = ( ( current TA - target TA ) * total volume ) / current TA

The recommended volume to treat is this minimum technical volume multiplied by 1.05.

The following formula is then used to calculate the mass of calcium carbonate (or Acidex® etc):

mass (kg) = ( ( current TA - target TA ) * total volume ) * ( ( 1 / 150.087 ) / 10 )

Where:

150.087 = the molecular mass of tartaric acid

10 = is simply a conversion to make the mass express in kg

**DSOS: =** Dissolved Solids Other than Sugar - note that if your density reading is from a hydrometer, using a value for DSOS is more important, if the reading is from a refractometer, you can probably assume no DSOS.

**Details:** This calculator works out how much sugar to add to a given volume of wine to raise it to a desired density (which we use as a measure of sugar content). For convenience it also calculates the estimated potential alcohol of the current must, and after the calculated chaptalisation. The estimated finishing gravity and correction for DSOS can be ignored if alcohol prediction is not required.

The alcohol calculation carried out here is identical to that carried out in the 'Alcohol Prediction (pre-ferment)' section.

The chaptalisation calculation is based on calculation of dissolved solids (grams per litre) as discussed in the 'Gravity/Density/Sugar Conversions' section. The difference between the desired and the current values is then simply multiplied by the number of litres to be chaptalised.

**Details:** This is a simple dilution calculator for water additions based on reducing the concentration of sugar, alcohol, acid etc. A common application is reducing the sugar concentration to reduce the eventual alcohol: In this case 'Current' is the estimated alcohol resulting from the present sugar concentration, and 'Desired' is the desired alcohol concentration. The calculator can be used similarly for any chosen concentration.

**Details:** This calculator calculates the point of fortification for making fortified wines with residual grape-sugar (e.g. Port). It accounts for both the obscuration of sugar, by the alcohol produced during fermentation, and the dilution of the residual sugar, during fortification.

This calculator finds the fortification point for making fortified wines which contain residual grape-sugar, such as Port. The formulae are derrived from the following:

Brix_in_fortified_wine = Brix_must / ( 1 + (1 / R) )

R = ( Alcohol_spirit - Alcohol_target ) / ( Alcohol_target - Alcohol_must)

Alcohol_in_fortified_wine = ( Brix_initial - Brix_current ) / 1.8

True-Brix = ( 97 * Brix_initial + 1200 * Brix_Current ) / 1297

These are combined and used to derive:

Fortification_Point = - ( 291 * Brix_initial * Alcohol_target + ( 3891 * Brix_final - 291 * Brix_initial ) * Alcohol_spirit - 2000 * Brix_final * Brix_initial ) / ( 3600 * Alcohol_target - 3600 * Alcohol_spirit + 2000 * Brix_final )

**Details:** This calculator works in the same way as a traditional Pearson's square. It is used to give the volume of spirit (of known alcohol content) to add to a volume of wine wine (of known alcohol content), to bring it to a desired alcohol content.

This calculator is simple, the calculation is exactly the same as a traditional Pearson's square. The following is the formula used:

spirit_to_add = vol_of_wine / ( ( spirit_alc_concentration - desired_alc_concentration ) / ( desired_alc_concentration - current_alc_concentration ) )

**Details:** This calculator makes fining trial and subsequent fining addition calculations quick and simple. After performing fining trials and deciding on an addition level, fill in all details and the volume of fining agent required will be calculated.

**Be sure to check all units,** the ones used here have been chosen for convenience in the majority of situations.

The first calculation is to find the concentration used in the trial:

concentration = (fining-agent-conc * (vol-fining-used / 1000)) / ((vol-wine + vol-fining-used) / 1000)

Where:

fining-agent-conc = concentration of the fining agent

vol-fining-used = the volume of fining agent used in the trial

vol-wine = the volume of wine used in the trial

Of course the divisions by 1000 are correcting for the units entered, the simplified equation is:

concentration = (fining-agent-conc * vol-fining-used) / (vol-wine + vol-fining-used)

This is an accurate calculation as the volume being divided by is the volume of wine AND the volume of the addition. This is often overlooked in calculations such as these, especially when performing them by hand. It is an important point to make, calculations from this equation will differ from quick calculations by hand.

The next calculation is to find how much of a solution of a specified concentration must be added to bring the concentration of the juice/wine to a desired concentration, this is discussed in the 'Additions in Solution' section.

**Details:** A very simple calculator to calculate the mass of a solid additive required to reach a specific concentration given a volume of juice/wine.

This is a very simple calculation:

mass-to-add = desired-concentration * volume / 1000

The division by 1000 is simply to provide the correct units.

**DAP = about 21% YAN (Yeast Assimilable Nitrogen)
PMS = 57% SO _{2} by mass**

**Details:**This calculator is for use with solids of which only a certain percentage is active. From the percentage, the desired addition level, and the volume of the juice/wine, the calculator will provide the mass of solid to add.

This is essentially the same as the solid addition calculation, except that the result is divided by the fraction of the solid that is active:

mass-to-add = (desired-concentration * volume ) / (percentage-active / 100)

**Details:** This calculator will calculate exactly how much of a solution of a given concentration to add to a given volume of juice/wine, to reach a desired concentration of the solute. For example, a solution of concentration 500mg/L is to be added to 100L of wine to give the wine a concentration of 10mg/L.

This calculation finds the volume of liquid, of a known concentration, which must be added to a given volume of wine/juice to bring the total concentration up to a desired value:

volume-to-add = (desired-concentration * wine-volume) / (additive-concentration - desired-concentration)

Note that this calculation takes into account the volume of the solution being added, so rather than adding 1L of 100mg/L additive to 100L of wine to give the wine a concentration of 1mg/L, the calculation shows that we need to add 1.010L.