It is widely accepted that the physical properties of nanostructures depend on the type of surface facets. For Au nanorods, the surface facets have a major influence on crucial effects such as reactivity and ligand adsorption and there has been controversy regarding facet indexing. Aberration-corrected electron microscopy is the ideal technique to study the atomic structure of nanomaterials. However, these images correspond to two-dimensional (2D) projections of 3D nano-objects, leading to an incomplete characterization. Recently, much progress was achieved in the field of atomic-resolution electron tomography, but it is still far from being a routinely used technique. Here we propose a methodology to measure the 3D atomic structure of free-standing nanoparticles, which we apply to characterize the surface facets of Au nanorods. This methodology is applicable to a broad range of nanocrystals, leading to unique insights concerning the connection between the structure and properties of nanostructures.