Nanoparticles are ubiquitous in nature. Their large surface areas and consequent chemical reactivity typically result in their aggregation into clusters. Their chemical and physical properties depend on cluster shapes, which are commonly complex and unknown. This is the first application of electron tomography with a transmission electron microscope to quantitatively determine the three-dimensional (3D) shapes, volumes, and surface areas of nanoparticle clusters. We use soot (black carbon, BC) nanoparticles as an example because it is a major contributor to environmental degradation and global climate change. To the extent that our samples are representative, we find that quantitative measurements of soot surface areas and volumes derived from electron tomograms differ from geometrically derived values by, respectively, almost one and two orders of magnitude. Global sensitivity studies suggest that the global burden and direct radiative forcing of fractal BC are only about 60% of the value if it is assumed that BC has a spherical shape.