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A scanning mobility particle sizer (SMPS) is a high resolution nanoparticle sizing system that is widely used as the standard method to measure airborne particle size distributions (PSD) in the size range 1 nm–1 μm. This paper addresses the problem to assess the uncertainty associated with PSD when a differential mobility analyzer (DMA) operates under scanning mode. The sources of uncertainty are described and then modeled either through experiments or knowledge extracted from the literature. Special care is brought to model the physics and to account for competing theories. Indeed, it appears that the modeling errors resulting from approximations of the physics can largely affect the final estimate of this indirect measurement, especially for quantities that are not measured during day-to-day experiments. The Monte Carlo method is used to compute the uncertainty associated with PSD. The method is tested against real data sets that are monosize polystyrene latex spheres (PSL) with nominal diameters of 100 nm, 200 nm and 450 nm. The median diameters and associated standard uncertainty of the aerosol particles are estimated as 101.22 nm  ±  0.18 nm, 204.39 nm  ±  1.71 nm and 443.87 nm  ±  1.52 nm with the new approach. Other statistical parameters, such as the mean diameter, the mode and the geometric mean and associated standard uncertainty, are also computed. These results are then compared with the results obtained by SMPS embedded software. [ABSTRACT FROM AUTHOR]