Influences of tip-convolution-induced artifacts on amplitude roughness measurements by atomic force microscopy under different surface geometrical parameters are analyzed. The concerned surface parameters are mainly standard deviation, correlation length and height distribution. The dependences of measured root-mean-square roughness on the main geometrical properties of both tip and surface are investigated by numerical simulation. It is found conditions for precise roughness measurements predicted through numerical simulations are in reasonable agreement with those obtained by simple analytical approximations. Measurements by atomic force microscopy tend to provide more accurate amplitude roughness values on rough surface with positive skewness.