The following publication describes a method for calculating a dielectric constant:
Determining dielectric constants using a parallel plate capacitor
T. T. Grove, M. F. Masters, and R. E. Miers
accepted 22 July 2004!
The availability of low cost digital multimeters capable of measuring capacitance has made parallel plate capacitor investigations common in the introductory laboratory. Typically, students add multiple thin sheets of dielectric material between conducting plates. The capacitance is measured and then plotted versus the reciprocal of the dielectric thickness ~the nominal plate separation!. We
explain why the experiment fails for small dielectric thickness and discuss an improved version of the experiment using dielectric sheets of various thicknesses rather than multiple thin sheets of a dielectric.