Electric permittivity has the dimension time to the 4th electric current squared per length cubed mass.  The SI composite unit of electric permittivity is the farad per meter.

Maple knows the units of electric permittivity listed in the following table.

An asterisk ( * ) indicates the default context, an at sign (@) indicates an abbreviation, and under the prefixes column, SI indicates that the unit takes all SI prefixes, IEC indicates that the unit takes IEC prefixes, and SI+ and SI- indicate that the unit takes only positive and negative SI prefixes, respectively.  Refer to a unit in the Units package by indexing the name or symbol with the context, for example, permittivity[Atomic] or kappa0[Atomic]; or, if the context is indicated as the default, by using only the unit name or symbol, for example, permittivity or kappa0.

The unit of electric permittivity is defined as follows.

An atomic unit of permittivity is defined as $\frac{1.\times {10}^7}{c^2}$ farad per meter where c is the magnitude of the speed of light, and is energy-equivalent to the dimensionless unit 1.

The permittivity of vacuum is defined as $\frac{1}{{\mathrm{\mu }}_0{c}^2}$ farad per meter where c is the magnitude of the speed of light and mu0 is the magnetic permeability of vacuum.

$\mathrm{convert}\left('\mathrm{permittivity}\left[\mathrm{Atomic}\right]'\,'\mathrm{dimensions}'\,'\mathrm{base}'=\mathrm{true}\right)$

$\frac{{\mathrm{electric\_current}}^2{\mathrm{time}}^4}{{\mathrm{length}}^3\mathrm{mass}}$

$\mathrm{convert}\left(1\,'\mathrm{units}'\,'\mathrm{permittivity}\left[\mathrm{Atomic}\right]'\,\frac{'F'}{'m'}\right)$

$\frac{2500000}{22468879468420441}$

$\mathrm{convert}\left(1\,'\mathrm{units}'\,'\mathrm{permittivity}\left[\mathrm{Atomic}\right]'\,1\,'\mathrm{energy}'\right)$

$1$

$\mathrm{convert}\left(1\,'\mathrm{units}'\,'\mathrm{\κ0}'\,'\mathrm{\ε0}'\right)$

$4\mathrm{\pi }$