The actual mathematical expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d is derived using Gauss’ Law and is derived in most physics textbooks. The result is Where ε_{o} is the permittivity of free space – air or a vacuum – which represents the willingness of a region to set up an electric field. ε_{o} has a value of 8.85 x 10^{-12} F/m. κ is called the dielectric constant and it measures how the electric field between the plates can be modified to allow the capacitor to have a greater capacitance (more charge per plate per volt) without any “sparking” occurring between the plates.