Method for measuring an AC current (I(t)) by means of a Rogowski coil that encloses a current path through which the AC current (I(t)) to be measured flows, said current periodically passing through continuous current values (I(ti)) and assuming a present current value (I) at a first time, in which the Rogowski coil in each case generates a corresponding first analogue AC voltage (Urc(t)), in which the first analogue AC voltage (Urc(t)) is converted into corresponding digital voltage values (Uti) that are continuously successive in time, wherein the digital voltage value (Uti) belonging to the first time is output as the present first voltage value, and in which the present first voltage value is provided with either a positive or a negative arithmetic sign in each case according to the arithmetic sign of the first analogue AC voltage (Urc(t)), characterized in that the present first voltage value is added to a first sum value (S1i) in each case and a present first sum value is therefore formed in each case, in that a present first mean value is formed in each case from the continuously successive first sum values (S1i) and is subtracted from the present first sum value, and a present second sum value is therefore formed, in that a present second mean value is formed in each case from the continuously successive second sum values (S2i) and is subtracted from the present second sum value, and a present third sum value is therefore formed, in that multiple third sum values (S3i) are used to calculate, through extrapolation, a prediction value (Vt1out) for a predefined output time (tlout) that is soonest after the first time, and in that the prediction value (Vt1out) is output at the predefined output time (t1out) in each case and a second analogue AC voltage (Up2out(t)) is formed from the continuously successive prediction values (Vtiout) at the associated continuously successive output times (tiout). in which the Rogowski coil in each case generates a corresponding first analogue AC voltage (Urc(t)), in which the first analogue AC voltage (Urc(t)) is converted into corresponding digital voltage values (Uti) that are continuously successive in time, wherein the digital voltage value (Uti) belonging to the first time is output as the present first voltage value, and in which the present first voltage value is provided with either a positive or a negative arithmetic sign in each case according to the arithmetic sign of the first analogue AC voltage (Urc(t)), characterized in that the present first voltage value is added to a first sum value (S1i) in each case and a present first sum value is therefore formed in each case, in that a present first mean value is formed in each case from the continuously successive first sum values (S1i) and is subtracted from the present first sum value, and a present second sum value is therefore formed, in that a present second mean value is formed in each case from the continuously successive second sum values (S2i) and is subtracted from the present second sum value, and a present third sum value is therefore formed, in that multiple third sum values (S3i) are used to calculate, through extrapolation, a prediction value (Vt1out) for a predefined output time (tlout) that is soonest after the first time, and in that the prediction value (Vt1out) is output at the predefined output time (t1out) in each case and a second analogue AC voltage (Up2out(t)) is formed from the continuously successive prediction values (Vtiout) at the associated continuously successive output times (tiout).