Export of sinking particles from the surface ocean is critical for carbon sequestration and for providing energy to the deep-ocean biosphere. The magnitude and spatial patterns of this flux have been estimated in the past by in situ flux observations, satellite-based algorithms, and ocean biogeochemical models; however, these estimates remain uncertain. Here, we use a novel machine learning reconstruction of global in situ ocean particle size spectra from Underwater Vision Profiler 5 (UVP5) measurements, to determine particulate carbon fluxes. We combine global maps of particle size distribution parameters for large sinking particles with observationally-constrained empirical relationships to calculate the sinking carbon flux from the euphotic zone and the wintertime mixed layer depth. Our flux reconstructions are comparable to prior estimates, but suggest a less variable seasonal cycle in the tropical ocean, and a more persistent export in the Southern Ocean than previously thought. Because our estimates are not bounded by a specific depth horizon, we reconstruct export at multiple depths, and find that export from the wintertime mixed layer globally exceeds that from the euphotic zone. Our estimates provide a baseline for more accurate understanding of particle cycles in the ocean, and open the way to fully three-dimensional global reconstructions of particle size spectra and fluxes in the ocean, supported by the growing database of optical observations.