The formation, evolution and dispersal processes of protoplanetary discs are investigated and the disc lifetime is estimated. The gravitational collapse of a pre-stellar core forms both a central star and a protoplanetary disc. The central star grows by accretion from the disc and irradiation by the central star heats up the disc and generates a thermal wind, which results in the disc's dispersal. Using the one-dimensional diffusion equation, we calculate the evolution of protoplanetary discs numerically. To calculate the disc evolution from formation to dispersal, we add source and sink terms that represent gas accretion from pre-stellar cores and photoevaporation, respectively. We find that the disc lifetimes of typical pre-stellar cores are around 2–4 million years (Myr). A pre-stellar core with high angular momentum forms a larger disc with a long lifetime, while a disc around an X-ray-luminous star has a short lifetime. Integrating disc lifetimes under various masses and angular velocities of pre-stellar cores and X-ray luminosities of young stellar objects, we obtain the disc fraction at a given stellar age and mean lifetime of the disc. Our model indicates that the mean lifetime of a protoplanetary disc is 3.7 Myr, which is consistent with the observational estimate from young stellar clusters. We also find that the dispersion of X-ray luminosity is needed to reproduce the observed disc fraction.