A relationship between the planar and spatial tortuosities of a statistically isotropic crack network in a clay soil is derived from the fact that connected cracks outline peds and are their boundaries. Connectedness, a parameter characterizing the crack network, determines this relationship. The two- and three-dimensional tortuosities vary from 1.5 to 2.2 and from 1.4 to 3.25, respectively, when connectedness decreases from unity to zero. A method proposed for processing two-dimensional images of crack networks enabled the estimation of two- and three-dimensional tortuosities of an assumed isotropic crack network. Two-dimensional images of seventeen different crack networks, available in the literature, were used to show the application of the proposed dependency between planar and spatial tortuosities