Db Scale

I have a problem that has been bugging me for some time now and I’d really like an answer for it, so if someone could help out, thanks. :)

Here is an image of what I’m talking about:

It’s a fragment of the dB scale taken from a sound file loaded into Sound Forge, and clearly shows that when converting the logarithmic dB scale to a linear one, -6 dB (or -6.02 to be exact) equals 50%. And -2.5 dB is half of that, or 25%. You can also find this out when normalising the sound file to a certain dB value in Sound Forge, as it also gives a linear percentage value alongside it.

Or here is a page with a list of dB values already converted in such a way:

http://www.execulink.com/~impact/audio_scale.htm

Now the thing I’d like to know is, what is the formula used for converting these logarithmic values to linear ones? Specifically, if you look at the above picture, -2.5 dB is clearly half of -6.02 dB, while -4.08 dB (or 4.1) is half of -12.04 dB.

In the first case I could convert -6.02 dB to get 50%, and multiplying this by 1.5 gives 75%, or -2.5 dB. But in the second case, multiplying -12.04 dB (25%) by 1.5 gives 37.5%, or -8.52 dB. So clearly there is some sort of logarithmic scale going on that I need to convert to a linear one.

So what kind of formula would I need in order to, say, find out the dB value of half of -18.06 dB as shown in the image? It would be half way between -4.08 and -6.02 dB, but is there a formula that I can use to work this out?

EDIT: Screwed up the title. It should really have read “converting between log and linear”

dB scale is a relative scale, it describes a relation. It is just a number, nondimensional.
So in order to calculate an absolute level, you need to set a reference level.
In your case, since you don’t want a voltage level but a percentage, your reference level is 100%.

So here’s your formula:

dB = 20 * log (out_level / ref_level)

example:

-6dB = 20 * log (50% / 100%)

or

50% = 100% * 10^(-6 / 20)

-6dB always halfs. No matter from where you start. Half of -18dB therefor is -24dB.

Thanks, but I’ve since found the answer long ago already. Thanks though! :D