coil - Mutual inductance vs coupling coefficient

Question regarding this and this question about mutual inductance and coupling coefficient.

I'm trying to analyse a two coil system:

It consists of two coils like in the picture with 2 cm air gap between them.

I want to find out the mutual inductance and the coupling coefficient. I'm confused, because, from my understanding, to calculate the mutual inductance, we need to know the coupling coefficient:

But to calculate the coupling coefficient, we need to know the mutual inductance.

Experimentaly, how should I measure coupling coefficient and mutual inductance between these two planar coils?

Answer

You can measure mutual inductance with only use of an LCR meter (or impedance analyzer). Use the following wiring while the coil position is fixed. Mutual inductance will be quarter of the difference between two readings.

^{simulate this circuit – Schematic created using CircuitLab}