  A semi-analytic method for quickly approximating the density-reduced critical
electric field for arbitrary mixtures of gases is proposed and validated.
Determination of this critical electric field is crucial for designing and
testing alternatives to SF$_6$ for insulating high voltage electrical
equipment. We outline the theoretical basis of the approximation formula from
electron fluid conservation equations, and demonstrate how for binary mixtures
the critical electric field can be computed from the transport data of
electrons in the pure gases. We demonstrate validity of the method in mixtures
of N$_2$ and O$_2$, and SF$_6$ and O$_2$. We conclude with an application of
the method to approximate the critical electric field for mixtures of SF$_6$
and HFO1234ze(E), which is a high interest mixture being actively studied for
high voltage insulation applications.
