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In sea-ice-covered areas, the sea ice floe size distribution (FSD) plays an important role in many processes affecting the coupled sea–ice–ocean–atmosphere system. Observations of the FSD are sparse – traditionally taken via a painstaking analysis of ice surface photography – and the seasonal and inter-annual evolution of floe size regionally and globally is largely unknown. Frequently, measured FSDs are assessed using a single number, the scaling exponent of the closest power-law fit to the observed floe size data, although in the absence of adequate datasets there have been limited tests of this "power-law hypothesis". Here we derive and explain a mathematical technique for deriving statistics of the sea ice FSD from polar-orbiting altimeters, satellites with sub-daily return times to polar regions with high along-track resolutions. Applied to the CryoSat-2 radar altimetric record, covering the period from 2010 to 2018, and incorporating 11 million individual floe samples, we produce the first pan-Arctic climatology and seasonal cycle of sea ice floe size statistics. We then perform the first pan-Arctic test of the power-law hypothesis, finding limited support in the range of floe sizes typically analyzed in photographic observational studies. We compare the seasonal variability in observed floe size to fully coupled climate model simulations including a prognostic floe size and thickness distribution and coupled wave model, finding good agreement in regions where modeled ocean surface waves cause sea ice fracture. [ABSTRACT FROM AUTHOR]