Fineness modulus is an important index to measure the fineness of sand. The current national standard fineness modulus formula does not involve particles with particle size below 0.15 mm. In this paper, the particles with particle size below 0.15 mm were further subdivided into 0.075~0.15 mm and smaller than 0.075 mm, and three new fineness modulus formulas were formed by incorporating these two grades into the fineness mode formula. Four different fineness modulus tests were randomly generated by rand function in MATLAB software, combined with the screening test of granite manufactured sand, tuff manufactured sand and nature sand, the advantages and disadvantages of different fineness modulus formulas were further verified. The approximate stone powder content of manufactured sand measured at the same time of screening. The empirical formula between the approximate stone powder content and the stone powder content measured by the standard method fitted by linear regression. Research shows that the addition of particles with particle size of 0.075~0.15 mm screening content to the numerator of the original fineness modulus formula is more conducive to characterize the fineness of sand. The difference between the content of approximate stone powder and standard stone powder is 1.346 6%.The surface of different sand samples is magnified by 100 times by SEM. It is found that the coarser the surface of sand samples, the greater the adsorption of stone powder, and the greater the volatility of the difference between approximate stone powder content and standard stone powder content.