I'm using the inductance calculator HERE: http://www.technick.net/public/code/cp_dpage.php?aiocp_dp=util_inductance_circle

It asks for "relative permeability of the medium" is this that of the copper wire I'm using (relative permeability: 1) or the core(air)?

 

Relative permeability in this case would refer to the core

 

Right, the permeability refers to the material that the magnetic circuit is passing through. It's analogous to the resistance of the material the electrical current flows through.

Folks tend to forget that a magnetic field needs to flow like a current as well, and needs a path to complete its circuit. Cuts in the circuit require sending the field through air, a poor "conductor" of magnetic field lines with a permeability of near 1.

 

If it is an air core coil, you can use 1.0 as the relative permeability.

Relative permeability is the magnetic analogy of dielectric constant. Its the flux density that results from a given magnetic force for a given material with respect to that of a vacuum.