Time/space series of natural variables (e.g., surface topography) are often self-affine, i.e., measurements taken at different resolutions have the same statistical characteristics when rescaled by factors that are generally different for the horizontal and vertical coordinates. Self-affinity implies that the standard deviation measured on a sample spanning a length w is proportional to wH=w2-D, where H is the Hurst exponent and D is the fractal dimension (1≤D≤2 for a fractal series). In this paper, a ''roughness-length'' method based on this property of self-affine series is presented. In practice, the root-mean-square roughness is computed in a number of windows of varying length w, and H is measured from the slope of a log-log plot of roughness versus w. Montecarlo simulations show that the fractal dimension as measured by the roughness-length method is approximately the same as that defined by the power spectrum. The roughness-length method is closely related to the grid fractal dimension, is simple to implement, and can be applied to non-uniformly spaced series. ¿American Geophysical Union 1990