# Calculations for mashes and dilutions

How to calculate how much water to add to alcohol to dilute it to the expected percentage? How to calculate how much alcohol will come out of the volume of sugar used? Today we will deal with useful formulas for this purpose, more precisely one very simple one:

C1 x V1 = C2 x V2

C1: is the concentration of the first system

V1: is its volume,

So if we have 5 liters of 10% alcohol in a jar, we'll describe it as C1= 10%, V1= 5l.

Similarly, C2 and V2 are the concentration and volume of the second system, in which we usually have our unknown. Translating into simpler language, it will be a description of our second vessel, whose volume we know, or the percentage we know, but we don't know how much space it occupies.

Wanting to estimate the volume and percentage of alcohol, we assume that we obtain on average 1 liter of 50% alcohol from one kilogram of sugar.

So if we have 5kg of sugar in our mash, we can expect that there will be 5l of 50% alcohol and water there. Using the formula C1 x V1 = C2 x V2, we calculate that 5l x 50% = Xl x Y%, where X= the volume of our mash, and Y is our calculated percentage.

In conclusion: If we have 5kg of sugar in a 25l mash, our formula looks like this:

Y[%]= (5l x 50%) / 25l

Y[%]= 250/25

Y= 10%

So we have a 25l 10% mash. How much raw alcohol will there be after distillation?

Similarly:

25l x 10% = P x Q%, where P= the volume of the raw distillate, and Q= its proof.

If we distilled 3.5l from these 25l, then applying the formula:

Q[%]= (25l x 10%)/ 3.5l

Q= ~71.5%

Now: how much water to add to get, for example, 40% vodka?

And again:

3.5l x 71.5%= xl x 40%

x=6.25l

6.25-3.5=2.75- so we need to add 2.75 liters of water to get 6.25l of 40% vodka.

Of course, there is a simpler way - pour the alcohol into the water and check with an alcohol meter. The cheapest alcohol meters can be bought here, and if you need indicators with high precision, check out the ultra-precise GOMAR alcohol meters. They have a range from 0 to 100% or - especially useful for spirits - a range of 70-100%.

Remember that alcohol meters indicate correctly only at the calibration temperature, so before measuring, make sure that the sample is exactly 20 degrees Celsius. The indication is possible only in a sample of pure ethanol in water, so measuring the strength of wine, tincture, or mash is not possible. To calculate the strength of wine, we need to know the initial and final sugar concentrations, which we measure with a saccharometer (divide the difference in BLG by 2).