https://doi.org/10.1351/goldbook.A00539
The average current density, \(j\), is defined by \[j = A^{-1}\ \int _{A}j_{x}\ \rm{d}A\] where \(A\) is the electrode area, \(j_{x}\) is the local current density and \(\rm{d}A\) is an infinitesimal surface element.