Is there a formula that can be used to determine how much liquid needs to be added to a distilled liquid to dilute it to a certain ABV?

Question

For example, say I have 500ml of 75% ABV (150 proof) alcohol and need to add water to dilute it to 35% ABV (70 proof), is there a simple formula where I can just plug in the numbers to determine how much I should add?

Answer 1

You need to ask yourself what doesn't change when water is added to the original solution. The answer is the absolute amount of alcohol stays the same.

So, let's calculate how much alcohol is initially present. If I start with 500 mL of solution at 75% ABV, the absolute volume of alcohol is 0.75 x 500 mL = 375 mL.

Now we want a solution that is 35% ABV, but the amount of alcohol in the new solution is still 375mL.

So, 0.35 x V_new = 375 mL where V_new is the new volume. If we solve for V_new and subtract the original volume of 500 mL, we get the amount of water to be added.

Regarding your wanting a simple formula for doing this calculation, it is better for you to understand the basic principle involved rather than memorizing a formula.