# What's the formula used for the gcpw calculation?

Hello!

Does anyone know the formula KiCad uses for calculating the Z_0 impedance in the built-in coplanar waveguide with ground plane calculator?

KiCad is an Open Source project. There are a few C++ files in the location below with â€śtranslineâ€ť in the filename.

So you can look it up yourself, or wait in the hope someone posts a more direct answer.

Did not manage to find the correct formula from the source code, but for those interested, I used the calculator available at Coplanar Waveguide With Ground Calculator for an approximation, which resulted in a 5% difference. Will be including the findings in my M.Eng, with KiCad having the edge over the formula from chemandy.

I had not looked inside the files before my first post, but just now I had a 10 minute peek, I saw mostly string building / menu drawing, but also files included from the transline directory.

And in there there are files full with formulaâ€™s, for example:

I donâ€™t know much about transmission lines, but I see tanh() functions and also ` sqrt( 1 - k2 * k2 )` so that is close at least.

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Thank you very much! At first glance, those formulas seem quite similar to those from Chemandy. Iâ€™m really tempted to do a mathematical comparison of the two if I can find the time before my deadline.

For those interested, here is the source from Chemandy: Transmission Line Design Handbook

These equations are always approximations. So long as you are using â€śnormalâ€ť impedances, dielectric thicknesses and spacings, 5% is achievable and good enough. For better than that, you need expensive substrate and very good plating and etching control.