In a method for determining a state variable of an electric arc furnace, especially for determining the level of the foamed slag (15) in a furnace, the energy supplied to the furnace is determined with the aid of at least one electric sensor while solid-borne noise is measured in the form of oscillations on the furnace. The state variable is determined by a transfer function which is determined by evaluating the measured oscillations and evaluating measured data of the electric sensor. The state of the foamed slag level can thus be reliably recognized and be monitored over time. The foamed slag level is decisive for the effectiveness with which energy is fed into the furnace. Furthermore, losses caused by radiation are reduced by covering the arc with the foamed slag. The improved measuring method allows the foamed slag level to be automatically controlled or regulated in a reliable manner.