If you want to know how much water to add to dilute your alcohol down, just multiply the amount of spirits you have by (strong/weak) - 1

eg: if you want to dilute 2L of 75% alcohol down to 40%, you will need to add 2 x ((75/40)-1) = 1.75L of water

If you want to know how much alcohol to use to make a known quantity, multiply the final amount by (weak/strong)

eg: to make 1.125L of 40% alcohol using spirit at 75%, you will need to use 1.125 x (40/75) = 0.6L of the 75% spirit, then top it up to 1.125L using water.

But its not always so ... Harry explains ...

It the UK it was laid down by an Act of Parliament in 1816 that "a quantity of 100 proof liquor would have the same weight as 12/13 ths of the same volume of pure water at 51° F." (That is twelve thirteenths) So,

100 proof (UK) = 57.06 %AbV

200 proof (US) = 100 %AbV = 175.25 proof (UK)

100 proof (US) = 50 %AbV = 87.6 proof (UK)

To avoid confusion, most alcohol for export from the UK is labelled at AbV.

A bit of history...

What is Proof?

Proof is another (older) measure of the strength of an alcoholic liquid. It had its origins in days when a simple test was needed that the liquor did indeed contain a *correct* measure (or more) of alcohol. And it was indeed a simple test.

Some of the liquor was poured over a little gunpowder and ignited. If the alcohol content was adequate, then it would burn 'just right' with a steady blue flame and eventually ignite the gunpowder. If there was insufficient alcohol then it would fizzle out and the gunpowder would be too wet to burn. The 'just right' condition 'proved' the liquor and it was declared to be '100 proof'.

This simple test was clearly cumbersome to perform and was later replaced by using a specially graduated hydrometer to measure the specific gravity. This was far more objective and allowed precise statements to be made as to how much different it was from being 100 proof. This gave rise to "under-proof" and "over-proof" measures.

Keep your powder dry (or wet it with the right stuff!) At one time (in the days of sailing ships, cannons and gunpowder) the makers of Plymouth Gin distilled a special gin for the Royal Navy. It was 57%AbV or 100 proof. Why? In order to keep it secure it was stored in the magazine close by the gunpowder. So, even if it leaked and wetted the gunpowder, at 100% proof the gunpowder would still explode. Though that need has been long gone, they still market the stuff!