A new empirical relation for the conventional measures of free surface roughness is proposed. Its geometric interpretation is a surface in three-dimensional space. A set of tests feasible for practical realization is discussed. Some available experimental and numerical results are used to reveal various qualitative features of the geometric surface. In particular, a reasonable assumption is that it is a ruled surface for a class of materials. A typical cross section of the surface, which is a curve, has an axis of symmetry if the roughening rate is independent of the sense of the strain rate normal to the material surface, where the roughness parameters should be predicted. The curve has a minimum at the axis of symmetry. Finally, there are two points, where the curve has a maximum. A simple analytic expression to specify the relation proposed for a given material is provided to fit experimental data.