$I={\displaystyle \underset{\text{S}}{\int }J\cdot e_{\text{n}}}\text{d}A$

where e_ndA is the vector surface element

NOTE 1 – The electric current through a surface is equal to the limit of the quotient of the electric charge transferred through that surface during a time interval by the duration of this interval when this duration tends to zero.

NOTE 2 – For charge carriers confined to a surface, the electric current is defined through a curve of this surface (see the note to term “lineic electric current”).