Convert percentage to range

Question

I have the following function to convert this function to percentage. The range of $y$ is $-120$ to $0$, so $-120 = 0\%$ and $0 = 100\%$.

$$percentage = 10^{(y + 160) / 80}$$

How do I go the other way by converting a percentage to the range $-120$ to $0$?

This doesn't quite work

$$y = 80 * log_{10}(percentage) - 160$$

Code to convert range $(-120, 0)$ to percentage

if (y > -120) {
    n = Math.pow(10, ((y + 160) / 80));
    if (n > 100) {
        n = 100;
    }
    if (n < 0) {
        n = 0;
    }
}

Thanks in advance

BT

IOW, $\mathrm{percentage} = \frac{5}{6}y+100$ wouldn't work? — Randall, Jan 11 '19 at 17:08
Your problem is that you can't take the log of $0$, but $0$ is a valid percentage. — Randall, Jan 11 '19 at 17:09
Or, the problem is that your formula does not convert $-120$ correctly. — Randall, Jan 11 '19 at 17:10
when you plug 1% into the second equation I get -160, not what I want — Big Tosspot, Jan 11 '19 at 17:15
maybe this is more appropriate to ask on code review, another forum. — ViktorStein, Jan 11 '19 at 17:29

Randall · Accepted Answer · 2019-01-11T17:53:43.953

2

Your first stated formula is incorrect: it does not do what you claim it does.

With $y=-120$, your formula gives $$ \mathrm{percentage} = 10^{0.5} =\sqrt{10} \neq 0. $$ So, your formula does NOT convert $-120$ to $0\%$. Instead, it converts it to roughly $3.16\%$. (It does, however, convert $y=0$ to $100\%$, but that's not good enough here.)

Anyway, because this part was wrong, this is why your log formula also fails.

If you just need any way at all to convert these, use something linear. So, $$ \mathrm{percentage} =\frac{5}{6}y+100 $$ in one direction and $$ y=\frac{6}{5}(\mathrm{percentage}-100) $$ in the other.

edited Jan 11 '19 at 17:53

answered Jan 11 '19 at 17:12

Randall

18,542
2
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Thanks Randall, if you have the time could you explain how you derived the 5/6 and the inverse 6/5, Thanks once again :) – Big Tosspot Jan 11 '19 at 17:52
You want pairs $(-120,0)$ and $(0,100)$, so figure out the slope and connect the dots. – Randall Jan 11 '19 at 17:53
1

Thanks, make sense, easy when you know how, much appreciated :) – Big Tosspot Jan 11 '19 at 18:51

score 0 · Answer 2 · answered Jan 11 '19 at 17:11

0

You have an issue which is that your mapping is not a bijection between $[-120, 0]$ and $[0, 100]$. So you cannot invert it to convert back our percentage into your initial value.

answered Jan 11 '19 at 17:11

Bermudes

455
4
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Convert percentage to range

2 Answers2