How to find value of beta = (mu*Cox)(W/L)/2 of MOSFET in ngspice
The SPICE deck determines these values; therefore, there is not a way to explicitly extract these values in ngspice.  If you have a level 0 model, you can easily get these from the model file; otherwise, you find that \$\mu\$, for instances changes.  What I would to is sweep the FET from the gate with the process voltage as \$V_{ds}\$.  You can then do a quadratic fit from threshold to about a volt beyond.