Using a compilation of experimental results obtained on different materials, the influence of the average roughness Rms on the precision σE (standard deviation) of the Young's modulus (Emean) determination using the Berkovich nanoindentation technique is studied for different depth penetration h. A power law dependence such as σE / Emean = β(Rms / h)n with n = 0.67, seems to be adapted. The value of this exponent, which is slightly function of the roughness fractal dimension, is in accordance with the works of Bobji et al. [M.S. Bobji, K. Shivakumar, H Alehossein, V. Venkateshwarlu, S.K. Biswas, Int. J. Rock Mech. and Min. Sci. 36 (1999) 399]. Nevertheless, the value of β is higher than the one given by those authors for millimetric scale of the relief and for a spherical indenter shape. For the hardness H, the following relation can be written, σH / Hmean = δσE / Emean with 1.2 ≤ δ ≤ 2 according to the material, the presence and the nature of the substrate.