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Given 100%, I need an equation to figure the equal steps that will occur between two percentages, where the first known percentage starts at 0% and the last known percentage ends at 100%.

For example, if the initial percentage is 17% and the final percentage is 3%, what will the graduated ( maybe linear? ) intervals be?

The simplest example that I can lay out without an equation would be if the first value is 40% and the end value is 10%. The final full set of percentages would be 40%, 30%, 20%, 10%. ( Total of 100% )

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    Finding some quirks making this illogical. Like, if both known percentages are 17, all intervals will be 17 but 100 is not divisible by 17. I'm thinking the two known percentages must have a specific relation to each other. – 2017-01-19
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    The same thing I was thinking of:max+min must divide 100. – 2017-01-19

2 Answers 2

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It sounds like you are looking for an arithmetic progression with the specified starting and ending values and summing to $100$. Let the starting number be $s$ and the ending number be $e$. The number of pairs of terms is then $\frac {100}{s+e}$. If this doesn't come out an integer or half integer you are stuck. $n=2\frac {100}{s+e}$ is the number of terms. Then the difference between the terms is $\frac {e-s}{n-1}$ as there are $n-1$ spaces between the terms. In your example, $s=17, e=3, n=10$ and the term difference is $-\frac {14}{9}$

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    [N74's answer](http://math.stackexchange.com/a/2105131/408423) is also correct but this one references the type of math we're dealing with and takes into account the direction ( start -> end vs. max or min ). – 2017-01-19
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Call $M$ the max of your list and $m$ the min, say $n=100/(M+m)$. Your step size will then be $p=(M-m)/(2n-1)$. This will only work if $2n$ is integer.