Electron backscatter diffraction (EBSD) techniques have been used to measure the dislocation density tensor for various materials. Orientation data are typically obtained over a planar array of measurement positions and the minimum dislocation content required to produce the observed lattice curvature is calculated as the geometrically necessary (or excess) dislocation density. The present work shows a comparison of measurements in two-dimensions and three-dimensions using a dual beam instrument (focused ion beam, electron beam) to obtain the data. The two-dimensional estimate is obviously lower than that obtained from three-dimensional data since the 2D analysis necessarily assumes that the third dimension has no curvature in the lattice. Effects of the free-surface on EBSD measurements are discussed in conjunction with comparisons against X-ray microdiffraction experiments and a discrete dislocation dynamics model. It is observed that the EBSD measurements are sensitive to free-surface effects that may yield dislocation density observations that are not consistent with that of the bulk material.