Bipolar diffusion charging of aerosol particles in the size range of 2.3-10 nm was studied experimentally. Charging probability for WOx nanoparticles as a function of particle size was measured using an Am-241 aerosol neutralizer for aerosol charging and a tandem DMA (Reischl type) with a VIE-06 Faraday cup electrometer for aerosol measurement. In spite of small deviations in the predictions from the theory of N. Fuchs on bipolar aerosol charging at 2-4 nm range, the theory was seen to be valid. Correction of the deviations may be performed by adjusting the free parameters in the theory (ion mass and mobility). As a rule of thumb, the charging probability of 2 nm particles was seen to be around 0.6% for negative and around 0.4% for positive particles.