Although the laser pulses with durations ranging from nanoseconds to femtoseconds and various pulse shapes are utilized for the Z-scan measurements, the influence of the temporal pulse shape on the measurement results is often neglected. In this paper, we tried to differentiate the influence of the temporal pulse shape on the common Z-scan technique with a small on-axis aperture in two cases: when the pulse peak intensity at the beam waist is known (for relatively long pulses), or when the total pulse energy and full width at half maximum (FWHM) of the correlation functions or FWHM of pulse durations are known (for short pulses).