[Math] How to calculate percentage value inside arbitrary range with results between -100% and +100%

optimizationpercentages

Sorry in advance if this is a very simple question and thanks for any help you might have.

I have a value of $3.82$.

I want to have a minimum and maximum difference allowance of say 1. So

min $= 3.32$
max $= 4.32$

I would like the min to be represented as -100% and max to be 100%. Essentially 3.82 would be 0%.

I have another value that is $3.54$. With the above in mind, how do I work out what percentage this number would be in my scale?

I did have a go using this formula but it gives me a scale of 0 to 200. Which isn't want I'm after, which is a scale of -100 to 100.
How to calculate percentage of value inside arbitrary range?

Thanks again!

Jim

Best Answer

It would make more sense to consider this symbolically

If you have min = $x$, max = $y$, then you have a range $y-x$

to calculate where a number $z$ lies on this range calculate

$200 \times (z-x)/(y-x) - 100$

For your example:

$ 200 \times(3.54-3.32 )/(4.32-3.32)-100 = -56$

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