These also exist as Footprint Wizards: Neurotech-Hub/KiCad-Plugins-8.0. Pad nets will be automatically tied.
\( L = \frac{K \cdot \mu_0 \cdot N^2 \cdot D_{\text{avg}}}{1 + K_1 \cdot \rho + K_2 \cdot \rho^2} \)
where, \( K = 2.34 \), \( K_1 = 2.75 \), \( K_2 = 0 \), \( \mu_0 = 4\pi \times 10^{-7} \) H/m, \( N \) is the number of turns, \( D_{\text{avg}} = \frac{L_{\text{antenna}} + W_{\text{antenna}}}{2} \) (meters), \( \rho = \frac{L_{\text{antenna}} - W_{\text{antenna}}}{L_{\text{antenna}} + W_{\text{antenna}}} \)
\( L = \frac{\mu_0 \cdot N^2 \cdot D_{\text{avg}}}{1 + 2.75 \cdot \frac{c}{2 \cdot D_{\text{avg}}}} \)
where, \( \mu_0 = 4\pi \times 10^{-7} \) H/m, \( N \) is the number of turns, \( D_{\text{avg}} = \frac{D_{\text{outer}} + D_{\text{inner}}}{2} \) (meters), \( c = D_{\text{outer}} - D_{\text{inner}} \) (meters)