Formulas for width of microstrip

Hello,

I am trying to make complex software tool which helps with design of resonators for analyzing dielectric properties but I have problem which I can not solve.

How to calculate width of microstrip if known parameters are: characteristic impedance, thickness of dielectric, thickness of trace and frequency. There a plenty of softwares that provide these calculations (synthesis of microstip) but there are no formulas which can be used by me (they are hidden so I do not know how this software works). I have found formulas where prior calculations you have to know effective dielectric constant but it is imposssible to calculate effective dielectric constant without known wifth of microstrip so I am quite lost.

Thank you for your time and respond.

If you don't find an analytical solution for the width, you'll solve it iteratively.

To write a "complex software", you should preferably have basic knowledge of numerical methods.

Thanks for your respond it is my back up plan and probably I will do it this way because it looks like this is the only way how to sort it out.