A method for the computation of spatial grain size distributions from intercept data based on a tetrakaidecahedron grain model is developed. The necessary inverse matrix is presented. The method is applied to a range of metallic and ceramic specimens. The derived distributions are analysed to show that they are not necessarily log-normal. Statistical techniques are applied to determine the minimum sample sizes and these are shown to increase as the distributions become more dispersed. The constant relating the average grain size to the average intercept length is also shown to be sensitive to the grain size distribution.