A method for scanning a work piece surface uses a coordinate measurement device. A probe element is brought into contact with the surface and the probe element is moved along the surface. The coordinate measurement device has a plurality of degrees of freedom, which are independent of one another, in the possible movements of the probe element with respect to the work piece. Maximum speeds which describe the maximum of a movement speed component of the probe element based on the respective degree of freedom are defined for the degrees of freedom. An estimated path on which the probe element is intended to move during scanning is predefined. The actual scanning path can differ from the estimated scanning path. A maximum scanning speed at which the estimated scanning path can be traveled with a constant speed of the probe element is determined.