According to the formula for the rate of heat conduction, $\frac{dQ}{dt} = kA \frac{\Delta T}{\Delta x}$, where $\frac{dQ}{dt}$ is the rate of heat flow (in Watts, W or $\text{J s}^{-1}$), $A$ is the area of cross-section (in $\text{m}^2$), $\Delta T$ is the temperature difference (in K), and $\Delta x$ is the thickness or length (in m).

Rearranging the formula for thermal conductivity ($k$), we get: $k = \frac{\frac{dQ}{dt} \cdot \Delta x}{A \cdot \Delta T}$

Substituting the SI units gives: $\text{Unit of } k = \frac{\text{W} \cdot \text{m}}{\text{m}^2 \cdot \text{K}} = \text{W m}^{-1} \text{K}^{-1}$.