We present a new method for quantifying three-dimensional silicate fabrics and the associated uncertainties from grain orientation data on three orthogonal sections. Our technique is applied to the orientation of crystallographic features and, hence, yields a fabric related to the lattice-preferred orientation, although the method could be applied to shape-preferred orientations or strain analysis based on passive linear markers. The orientation data for each section are represented by their cumulative distribution function, and an iterative procedure is used to find the symmetric second-rank strain tensor that will simultaneously satisfy the cumulative distribution functions observed on each section. For samples with well-developed fabrics, this technique provides a much closer match to the sectional data than do previous techniques based on eigenparameter analysis of two-dimensional orientation data. Robust uncertainty estimates are derived from a non-parametric bootstrap resampling scheme. The method is applied to two cumulates: one with a well-developed fabric and the other with a weak fabric, from the Stillwater complex, Montana. The silicate petrofabric orientations obtained for these samples compare favorably with independent direct estimates of the volume fabric from electron backscatter diffraction and magnetic techniques.