Magnetic holes (MHs), characteristic structures where the magnetic field magnitude decreases significantly, have been frequently observed in space plasmas. Particularly, small size magnetic holes (SSMHs) which the scale is less than or close to the proton gyroradius are recently detected in the magnetospheric plasma sheet. In this study of Cluster observations, by the timing method, the minimum directional difference (MDD) method, and the spatiotemporal difference (STD) method, we obtain the propagation velocity of SSMHs in the plasma flow frame. Furthermore, based on electron magnetohydrodynamics (EMHD) theory we calculate the velocity, width, and depth of the electron solitary wave and compare it to SSMH observations. The result shows a good accord between the theory and the observation. Key Points The velocity of small size magnetic holes in the plasma flow is calculated The results show that they are propagating in the plasma flow The structure velocity agrees with the electron soliton velocity