A self-calibrating sigma-delta converter (SCADC) functions in a calibration mode and in an operational mode. In the calibration mode, a test circuit of the SCADC generates test signals that are periodic rectangular voltage waveforms. Each test signal has a dc component with a precise voltage amplitude, as well as harmonic components. A low-pass filter of a sigma-delta converter (SDC) within the SCADC filters out the harmonic components. A digital calibration processing circuit within the SCADC uses the precise voltage amplitudes to generate digital correction factors that compensate for dc offset error, gain error and INL error of the SDC. In the operational mode, the SDC receives an analog operational signal and outputs an operational digital data stream. The digital calibration processing circuit uses the correction factors to compensate for dc offset error, gain error and INL error in the operational digital data stream and outputs a corrected digital data stream.