Electric wave

VF equals the reciprocal of the square root of the dielectric constant (relative permittivity), ${\displaystyle \kappa }$ or ${\displaystyle \epsilon _{\mathrm {r} }}$, of the material through which the signal passes:

${\displaystyle \mathrm {VF} ={\frac {1}{\sqrt {\kappa }}}\ }$

in the usual case where the relative permeability, ${\displaystyle \mu _{\mathrm {r} }}$, is 1. In the most general case:

${\displaystyle \mathrm {VF} ={\frac {1}{\sqrt {\mu _{\mathrm {r} }\epsilon _{\mathrm {r} }}}}\ }$

which includes unusual magnetic conducting materials, such as ferrite.

The velocity factor for a lossless transmission line is given by:

${\displaystyle \mathrm {VF} ={\frac {1}{c_{\mathrm {0} }{\sqrt {L'C'}}}}\ }$

where ${\displaystyle L'}$ is the distributed inductance (in henries per unit length), ${\displaystyle C'}$ is the capacitance between the two conductors (in farads per unit length), and ${\displaystyle c_{\mathrm {0} }}$ is the speed of light in vacuum.

Optical wave

VF equals the reciprocal of the refractive index ${\displaystyle {n}}$ of the medium, usually optical fiber.

${\displaystyle \mathrm {VF} ={\frac {1}{n}}\ }$