# Calculate percentage on negative to positive scale [closed]

Scale 1:
-5  -4  -3  -2  -1  0   1   2   3   4   5
Scale 2:
1   2   3   4   5   6   7   8   9   10  11


How do I calculate the percentage of value X in Scale 1 when 0 is a valid value on the scale?

Ex. 3 in Scale 2 would be 3/11*100 = 27.3%

So whats the function to get -3 in Scale 1 to be 27.3% of its scales total steps?

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## closed as not a real question by Dominic Michaelis, Did, rschwieb, Jim, JSchlatherMar 14 '13 at 17:43

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

what is the value x? Sorry but i don't unterstand your question – Dominic Michaelis Mar 14 '13 at 16:23
Value x = if x is 3 in scale 2 then X is -3 on scale 1. If its 6 on scale 2 then its 0 on scale 1. – mdc Mar 14 '13 at 16:56
Yet another unjustified closure of a question with an obvious interpretation, lacking even the excuse of lack of involvement by the OP. It was ‘reasonably answered in its current form’. I have of course voted to reopen. – Brian M. Scott Mar 14 '13 at 19:47

Scale $1$ runs from $-5$ to $5$ in steps of $1$ unit, so it has $11$ values. $-3$ is the third value. Thus, $3$ of the $11$ values are less than or equal to $-3$, so $\frac3{11}$ of the values are less than or equal to $-3$. If you convert this fraction to a percentage, you get $27.3$% when you round to one decimal place.

More generally, if a scale runs from $a$ to $b$ in steps of size $d$, it has $\frac{b-a}d+1$ values. If $v$ is one of the values, there are $\frac{v-a}d$ values smaller than $v$, so $v$ is the $\left(\frac{v-a}d+1\right)$-st value.

In Scale $1$, for instance, $a=-5$, $v=-3$, and $d=1$, so $-3$ is the $\left(\frac{-3-(-5)}1+1\right)$-st value or, after you do the arithmetic, the $3$-rd value. (Of course in this case we don’t need the formula: we can easily see that $-3$ is the $3$-rd value.)

Thus, we have altogether $\frac{b-a}d+1$ values, and $\frac{v-a}d+1$ of them are less than or equal to $v$, so the fraction of them that are less than or equal to $v$ is

$$\frac{\frac{v-a}d+1}{\frac{b-a}d+1}=\frac{v-a+d}{b-a+d}\;,$$

and you can convert this to a percentage simply by multiplying by $100$. In the example with $a=-5$, $b=5$, $d=1$, and $v=-3$, this formula yields the fraction

$$\frac{-3-(-5)+1}{5-(-5)+1}=\frac3{11}\;,$$

as we knew it should.

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Great answer, thank you! – mdc Mar 15 '13 at 9:52
@mdc: You’re welcome! – Brian M. Scott Mar 15 '13 at 10:11