The invention relates to a device for measuring currents (3) in the conductors of a sheathed cable of a polyphase network, comprising at least three magnetic sensors (300) arranged around a central hole (312) through which the cable to be measured is intended to pass, the number of conductors in said cable being less than the number of sensors, and a calculation device (330) configured to: access a library of matrices [K] and [K]+, where [K]+ is a pseudo-inverse matrix of matrix [K]; form a vector [B] including a magnetic field measurement for each of the sensors; for various cable configurations and various angular positions of the sensors relative to the cables, calculate a residual vector [R] = [K].[K]+.[B] - [B]; select the matrix [K]+ for which the norm of the vector [R] is minimal; and calculate [1] = [K]+.[B], where [K]+ is the selected matrix.
