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There are a lot of free tools that can do the planar structure impedance calculation and synthesis work. What you want to know is the synthesis one. A simple way is to use some emprical design formulas available in many text books. You may also want to refer to: http://mcalc.sourceforge.net/index.html for some knowledge(see the selected reference section).
Dr Howard Johnson covers the kind of information you want in his books "High-Speed Digital Design-A Handbook of Black Magic" and " High-Speed Signal Propagation-Advanced Black Magic".
Look at the pages in the following URLs. There are equations that can be plugged into M@thC@d to calculate the sort of thing you are interested in. The results aren't as accurate as modeling in one of the high speed synthesis programs, but they get you in the ballpark for most real world problems.
What you need is Hyperyinx to help you. Very good program. A common impedance is 50 Ohms. I usually choose a trace width of 10mil above a plane, then use Hyperlynx and the layer stack. Hyperlynx field solver will calculate the required stack up spacings to achieve the target impedance.
As I've mentioned, basically there are two aspects of impedance related problems:
1. Impedance calculation:
known the phyical parameters such as dielectric thickness, dielectric constant, trace width etc to get the electrical (or so called technical) parameter (here is impedance).
2. Impedance synthesis:
target for certain specified impedance value, say, 50Ohm or 100Ohm, what we need to know is what kind of combinations of physical(or so-called geometrical) parameters such as trace width, dielectric thickness etc can give us the targeted value. This is so-called impedance synthesis.
A lot of freeware and commercial package can do a good job. However, some of them can only have the "impedance calculation function" and some have both the "calculation" and "synthesis" function. And some of them based on analytical method(using empirical equations) such as Tline, LineCalc inside Agilent ADS and some are EM quasi-static field solvers such as Hyperyinx, Ansoft Q3D/2D, Polar Si6xx series etc.
For general purpose use, most of the freewares can do a good job for you such as the one I posted, the one from Agilent: AppCAD http://www.hp.woodshot.com/ and bunches of tools from the website.
I agree APPCAD is good and free. I believe MWO (ARL) have a free one too. Or
it comes with the trial version of MicroWave Office. But I would also suggest
that you think about using Rogers board and their line calc.
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