Future weak lensing surveys potentially hold the highest statistical power for constraining cosmological parameters compared to other cosmological probes. The statistical power of a weak lensing survey is determined by the sky coverage, the inverse of the noise in shear measurements and the galaxy number density. The combination of the latter two factors is often expressed in terms of n eff - the 'effective number density of galaxies used for weak lensing measurements'. In this work, we estimate n eff for the Large Synoptic Survey Telescope (LSST) project, the most powerful ground-based lensing survey planned for the next two decades. We investigate how the following factors affect the resulting n eff of the survey with detailed simulations: (1) survey time, (2) shear measurement algorithm, (3) algorithm for combining multiple exposures, (4) inclusion of data from multiple filter bands, (5) redshift distribution of the galaxies and (6) masking and blending. For the first time, we quantify in a general weak lensing analysis pipeline the sensitivity of n eff to the above factors. We find that with current weak lensing algorithms, expected distributions of observing parameters, and all lensing data (r and i band, covering 18 000 degree2 of sky) for LSST, n eff 37 arcmin−2 before considering blending and masking, n eff 31 arcmin−2 when rejecting seriously blended galaxies and n eff 26 arcmin−2 when considering an additional 15 per cent loss of galaxies due to masking. With future improvements in weak lensing algorithms, these values could be expected to increase by up to 20 per cent. Throughout the paper, we also stress the ways in which n eff depends on our ability to understand and control systematic effects in the measurements.