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Alcohol is conserved when diluting, so the final volume is pure alcohol divided by the target strength fraction, and water to add is the difference from the starting volume. In practice ethanol and water contract slightly on mixing, so the true final volume is a little less and strength must be verified after blending.
Proofing down
Final volume = spirit volume x current ABV / target ABV; water = final volume - spirit volume
Declared alcohol strength is legally regulated with narrow tolerances and determines excise duty. Verify by an approved method at the reference temperature.
Volume contraction on mixing means the arithmetic slightly under-predicts strength. Custody and labelling require measurement with a calibrated hydrometer or density meter at a controlled temperature.
Yes. Demineralised or very soft water avoids haze from calcium and magnesium reacting with fatty acids, and avoids chlorine and off-flavours. Hard tap water can cloud a spirit permanently.