The numerical diffusion of the discretization of the convection term is investigated. The quantitative evaluation method for the numerical diffusion is proposed. The method evaluates the influence of the numerical diffusion to the shape and the thickness of the free surface by the rate of dullness and blur, respectively. High-order schemes are compared with each other using the proposed method in a two-dimensional simple flow and a two-dimensional collapsing water column. As a result, Chakravarthy-Osher (CO) method and Compressive Interface Capture Scheme for Arbitrary Meshes (CICSAM) are more accurate than other schemes in a two-dimensional simple flow. In the collapsing water column, CICSAM is more accurate than CO. CICSAM with the anti-diffusion operation is lower than CICSAM in the rate of dullness and blur. It is shown that the proposal quantitative evaluation method is able to quantify the numerical diffusion.