Tranconductance formula
\$gm0\$ (for the JFET only) is a transconductance at \$Vgs = 0V\$ and \$I_D = I_{DSS}\$. 

That means that \$gm\$ for |Vgs|&lt; 0 and Id &lt; Idss is equal to

$$
gm = gm0 *\left ( 1-\frac{V_{GS}}{V_P} \right )= \frac{2I_{DSS}}{|V_P|}*\left ( 1-\frac{V_{GS}}{V_T} \right )  
$$

Also notice that \$ V_P = V_{GS(off)} \$ 

Sometimes we use alternative formula 

$$
gm = \frac{2I_{DSS}}{|V_P|}*\sqrt{\frac{I_D}{I_{DSS}}}  
$$

For the MOSFET (enhancement) if we assume that in saturation (active region) the drain current is equal to 
$$
I_D = K*\left ( V_{GS} - V_{P}  \right )^2  
$$ 
and we definde 
$$ 
K = \frac{I_D}{(V_{GS} - V_{P})^2}
$$

the gm is equal to: 

$$
gm = 2\sqrt{K*I_D}
$$

Or 

$$
gm=2K\left ( V_{GS} - V_{P}  \right )
$$