  The Neumann Equation of State (EQS) allows obtaining the value of the surface
free energy of a solid ${\gamma}_{SV}$ from the contact angle $({\theta})$ of a
probe liquid with known surface tension ${\gamma}_{LV}$. The value of
${\gamma}_{SV}$ is obtained by numerical methods solving the corresponding EQS.
In this work, we analyzed the discrepancies between the values of
${\gamma}_{SV}$ obtained using the three versions of the EQS reported in the
literature. The condition number of the different EQS was used to analyze their
sensitivity to the uncertainty in the ${\theta}$ values. Polynomials fit to one
of these versions of EQS are proposed to obtain values of ${\gamma}_{SV}$
directly from contact angles $({\gamma}_{SV} ({\theta}))$ of particular probe
liquids. Finally, a general adjusted polynomial is presented to obtain the
values of ${\gamma}_{SV}$ not restricted to a particular probe liquid
$({\gamma}_{SV}({\theta},{\gamma}_{LV}))$. Results showed that the three
versions of EQS present non-negligible discrepancies, especially at high values
of ${\theta}$. The sensitivity of the EQS to the uncertainty in the values of
${\theta}$ is very similar in the three versions and depends on the probe
liquid used (greater sensitivity at higher ${\gamma}_{LV})$ and on the value of
${\gamma}_{SV}$ of the solid (greater sensitivity at lower ${\gamma}_{SV})$.
The discrepancy of the values obtained by numerical resolution of both the
fifth-order fit polynomials and the general fit polynomial was low, no larger
than ${\pm}0.40\,mJ/m^{2}$. The polynomials obtained allow the analysis and
propagation of the uncertainty of the input variables in the determination of
${\gamma}_{SV}$ in a simple and fast way.
