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The voltage flicker is one of the major power quality disturbances in a weak power system. Better measurement and limitation techniques are always desired. An effective and accurate calculation method is presented to obtain the voltage flicker components and the 10 Hz equivalent value. By using the indirect demodulation method, the RMS values of a voltage waveform are calculated cycle by cycle to obtain the envelope. Then the fast Fourier transform (FFT) is used to obtain the flicker components. This method can increase the computing speed and reduce the hardware requirement in a power quality instrument when the FFT is used. The effects of sampling rate, harmonics, and system frequency shifting are investigated. The latter two are common disturbances in addition to the voltage flicker when arc furnace loads are connected in a weak power system. A calibration procedure is used to improve the frequency leakage effect and increase the calculation accuracy. The calculation results from given voltage flicker waveforms and field measured waveforms reveal the effectiveness of the proposed method. It can be used in both 50 and 60 Hz systems.