An analog-to-digital converter (ADC) exhibiting an uncorrected non-linear transfer function receives measured analog voltage amplitudes and outputs uncorrected digital values. A calibration circuit receives each uncorrected digital value and outputs a corrected digital value. The measured analog voltage amplitudes received by the ADC and the corresponding corrected digital values output by the calibration circuit define points approximating an ideal linear transfer function of the ADC. The calibration circuit performs piecewise-linear approximation of the uncorrected transfer function and associates each uncorrected digital value with the applicable linear segment that passes through a segment endpoint on the uncorrected transfer function. The calibration circuit calculates each corrected digital value using calibration coefficients associated with the applicable linear segment, such as the slope of the linear segment. The calibration circuit determines the calibration coefficients by calculating the second derivative of the uncorrected transfer function. The calibration coefficients are stored in non-volatile memory.