Blending a stronger liquid down to a target strength is one of the oldest bits of arithmetic in food and drink, and it has a name: Pearson's square. This alcohol dilution calculator applies it to alcohol by volume, telling you how much water — or how much of a weaker liquid — to add to a known volume at a known strength to land on a target. It also tells you the thing most dilution calculators leave out, which is that the finished volume will not be quite what the addition suggests.
Arb Digital builds free tools that state their own limits. The square is exact as a statement about how much pure alcohol is present. It is only approximate as a statement about the strength of the finished liquid, because alcohol by volume is defined on a volume that changes when you mix. The page below explains where that error comes from and roughly how large it is.
What This Alcohol Dilution Calculator Does
Enter a starting strength and volume, a target strength, and the strength of whatever you are blending in. The calculator returns the volume of diluent to add, the resulting volume if volumes were simply additive, the blend ratio expressed as spirit to diluent, and the amount of pure alcohol present, which does not change when you dilute. It also converts a serve of the finished blend into UK alcohol units, purely as a reference point.
Setting the diluent strength above zero turns it into a general blending calculator: a 60% spirit blended with a 20% liqueur to reach 35%, for example, works on exactly the same square. The only requirement is that the target sits between the two strengths.
How to Use It
- Enter the true starting strength. A label figure is a legal declaration within a tolerance, not a measurement of the bottle in your hand.
- Enter the starting volume in millilitres. Weighing is more reliable than reading a jug, if you have a scale.
- Enter your target strength and the diluent strength, using zero for water.
- Add the diluent gradually and check as you go rather than pouring the whole calculated amount in one go.
- Measure the finished strength with a hydrometer at the correct reference temperature if the exact figure matters.
Pearson's Square and a Worked Example
The square is a bookkeeping device for a conservation law: the alcohol in the blend equals the alcohol in each part. Written as a formula, the volume of diluent to add is Vadd = V₁ × (C₁ − Ctarget) ÷ (Ctarget − Cdiluent), where C values are strengths as percentages.
Take the defaults. A 750 mL bottle at 40% taken down to 20% with water gives 750 × (40 − 20) ÷ (20 − 0) = 750 × 20 ÷ 20 = 750 mL of water. The ratio is 1:1, the ideal final volume is 1,500 mL, and the pure alcohol is 750 × 0.40 = 300 mL, unchanged by the dilution. Check it: 300 ÷ 1,500 = 20%. A second case shows the general form — blending a 60% spirit into a 20% liqueur to reach 35% gives, for one litre of the 60%, 1,000 × (60 − 35) ÷ (35 − 20) = 1,667 mL of the liqueur.
Why the Volumes Do Not Add Up
This is the part the square cannot see. Ethanol and water do not mix ideally: the molecules pack more closely together than they do apart, so the mixture occupies less space than the sum of its ingredients. The classic demonstration is that 50 mL of ethanol combined with 50 mL of water gives roughly 96 mL rather than 100 mL. The contraction is largest in the middle of the range and shrinks towards either pure end.
That matters because alcohol by volume is a ratio of volumes. The quantity of pure alcohol is genuinely conserved, so the numerator of the ABV fraction is exactly right; it is the denominator, the finished volume, that comes out smaller than expected. The practical consequence is that a blend calculated to 20% will typically measure very slightly above it. The effect is small — on the order of a per cent or so of the reading, not a wholesale error — and it is why anyone who needs the number to be right measures the result rather than trusting the arithmetic.
Temperature, Hydrometers and What ABV Is Defined Against
Strength is defined at a reference temperature, and the reference is not the same everywhere: much of the world uses 20 °C, while the United States gauges distilled spirits at 60 °F, which is 15.56 °C. The Alcohol and Tobacco Tax and Trade Bureau publishes the gauging tables and procedures used for that in its Gauging Manual, and the corresponding regulations sit in Title 27 of the Code of Federal Regulations, Part 30.
The practical point is that a hydrometer reading taken at the wrong temperature is wrong, and warm liquid reads low. Blending also releases a little heat, so a freshly mixed batch will read differently from the same batch measured an hour later at room temperature. If you want a strength figure you can rely on, let the blend settle to the reference temperature before reading it, or correct the reading using published tables. Our specific gravity calculator covers the density side of the same measurement problem.
A Note on What This Page Is Not For
This is a blending calculator for liquids you already legally possess. Producing spirits at home is illegal in many jurisdictions, including without a licence in the United States and the United Kingdom, and this page gives no distilling instruction of any kind and is not a guide to producing alcohol.
It is also worth being straightforward about the substance itself. The World Health Organization's fact sheet on alcohol states that there is no form of alcohol consumption that is risk-free and that even low levels carry some risk, attributing roughly 2.6 million deaths globally in 2019 to alcohol and linking it causally to over 200 diseases and conditions. Diluting a drink lowers the strength of what is in the glass; it does not change how much alcohol you consume unless you also drink less of it.
Units, Serves and Keeping Track
The units box exists because strength and dose are easy to confuse. The NHS defines a unit as strength in ABV multiplied by volume in millilitres, divided by 1,000, and advises not regularly drinking more than 14 units a week, spread over three or more days, with several drink-free days for anyone cutting down. A 25 mL serve of a 20% blend is 0.5 units; the same 25 mL at 40% is 1.0 unit. Halving the strength halves the units in a fixed serve — but pouring a double undoes it exactly.
Arb Digital builds content and tools for categories where claims are constrained and getting a figure wrong is a real problem. Tell us what you are publishing and we will show you how we would frame it.
Browse Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Assuming volumes add. Ethanol and water contract on mixing, so the finished liquid measures less than the sum of the parts.
- Trusting the label strength as a measurement. A declared ABV is a legal figure within a tolerance, not a reading of your bottle.
- Reading a hydrometer at the wrong temperature. Strength is defined at a reference temperature and warm liquid reads low.
- Setting a target outside the two strengths. A blend can only land between the strengths of its ingredients.
- Confusing strength with dose. A weaker drink in a bigger glass is not less alcohol.
Related Free Tools From Arb Digital
To derive an ABV from fermentation gravity readings rather than change an existing one, use the ABV calculator; to convert a finished drink into standard units, the alcohol units calculator, and for blood alcohol modelling the BAC calculator. For dilution problems outside drinks, the dilution ratio calculator and the solution dilution calculator handle ratios and molar concentrations, while the specific gravity calculator and percentage calculator cover the measurement and the arithmetic. The free online tools hub lists everything else.
Frequently Asked Questions
Multiply the starting volume by the difference between the starting and target strengths, then divide by the difference between the target and the diluent strength. Taking 750 mL at 40% down to 20% with water needs 750 mL of water, giving a one to one blend.
A simple bookkeeping method for working out the proportions of two liquids of known concentration needed to reach a target concentration. It works for anything measured on a linear scale, which is why the same square is used for blending wine, adjusting feed rations and diluting spirits.
Ethanol and water contract when mixed, because the molecules pack more closely together than they do apart. Fifty millilitres of ethanol and fifty of water give roughly ninety-six millilitres. The contraction is largest in the middle of the range and small near either pure end.
No. The quantity of pure alcohol is unchanged by adding water; only its concentration falls. That is why the pure alcohol figure in the results stays the same as you move the target strength.
Alcohol by volume is defined at a reference temperature, commonly 20 °C, though the United States gauges distilled spirits at 60 °F. Hydrometers read low in warm liquid, and blending itself releases a little heat, so a freshly mixed batch reads differently from the same batch at room temperature.
Yes. Set the diluent strength to the ABV of the weaker liquid and the same square applies. The only requirement is that the target strength sits between the strengths of the two ingredients.
No. It is a blending calculator for liquids you already legally hold. Producing spirits at home is illegal in many jurisdictions, including without a licence in the United States and the United Kingdom, and this page gives no distilling instruction.
This tool performs blending arithmetic and does not verify the strength of anything you mix. Alcohol by volume is defined at a reference temperature and mixed volumes contract, so measure a finished blend rather than relying on a calculated figure. Producing distilled spirits at home is illegal in many jurisdictions. The World Health Organization states that no level of alcohol consumption is risk-free; speak to a clinician or a national alcohol support service about your own drinking.
