Dilute alcohol
If you want to turn a higher alcohol percentage into a lower one (such as 91% alcohol to 70% alcohol) for sanitizer or anything else.
Find the amount of water (w) to add
a = alcohol % before you add water
b = alcohol % after you add water
c = a/b
d = c-1
e = amount of alcohol you have
w = amount of water to add to the alcohol you have, in order to make the diluted alcohol you want
So...
a/b = c
c-1 = d
d×e = w
Also, w+e = the amount of diluted alcohol you'll have made after mixing (shaken, not stirred).
See an example
Find the amount of water needed to dilute 16 fl oz of 91% alcohol, so that you get 70% alcohol...
91/70 = 1.3
1.3-1 = .3
.3×16 = 4.8
So, you will add 4.8 fl oz of water to 16 fl oz of 91% alcohol to make it 20.8 fl oz of 70% alcohol.
Further explanations
What made sense to me
To explain the example above, if you start with a total of 16 fl oz of 91% alcohol, then it contains 14.56 fl oz of pure 100% alcohol (because 16×.91 = 14.56, therefore 91% of 16 fl oz is 14.56 fl oz). The rest, 1.44 fl oz, is water.
The total amount of 70% alcohol that you're trying to make (let's call that "t") would contain (t×.70) fl oz of pure 100% alcohol.
100% = 100%
So, t×.70 = 16×.91
Therefore, t×.70 = 14.56
Therefore, t = 14.56/.70
Therefore, t = 20.8 fl oz of 70% alcohol
So, to make 20.8 fl oz of 70% alcohol, how much water will you need? Since we already have 16 fl oz of 90% alcohol, we'll subtract that to find out...
20.8 - 16 = 4.8 fl oz of water
That's why you'll add 4.8 fl oz of water to 16 fl oz of 91% alcohol in order to make 20.8 fl oz of 70% alcohol.
Still confused?
It happens to us all. Here are some more folks explaining in additional ways.
Why dilute? Isn't a higher alcohol % better for sanitizing?
Solutions of about 70% alcohol tend to sanitize best. A much lower percentage may not be strong enough to kill a virus (such as COVID, flu, etc.), but a much higher percentage can evaporate too quickly to be effective.
This is what makes 70% a sweet spot.
Tip: You can also just buy alcohol at 70% open_in_new to avoid math and mixing.