# Convert Between Loss Tangent and Conductivity

It is possible to convert between the loss tangent and conductivity description of the material losses at a single frequency. This application macro performs the calculation and can be used in CADFEKO and POSTFEKO.

Given the frequency, relative permittivity and either the loss tangent or the conductivity of a material, the remaining parameter can be calculated through the relationship

(1) $\mathrm{tan}\delta =\frac{\sigma }{\omega {\epsilon }_{0}{\epsilon }_{r}}$

where $\mathrm{tan}\delta$ is the loss tangent, $\sigma$ is the conductivity, $\omega =2\pi f$ is the angular frequency, ${\epsilon }_{0}$ is the free space permittivity and, ${\epsilon }_{r}$ is the real part of the relative complex permittivity of the medium.

It is often required to convert between these parameters when using the FDTD solver, since frequency-dependent materials are not supported for FDTD.