The formation of atmospheric aerosol particles (homogeneous nucleation, forming of stable clusters ~1 nm in size), their subsequent growth to detectable sizes (>3 nm), and to the size of cloud condensation nuclei, remains one of the least understood atmospheric processes upon which global climate change critically depends. However, a quantitative model explanation for the growth of freshly formed aerosols has been missing. In this study, we present observations explaining the nucleation mode (3--25 nm) growth. Aerosol particles typically grow from 3 nm to 60--70 nm during a day, while their non-volatile cores grow by 10--20 nm as well. The total particle growth rate is 2--8 nm/h while the non-volatile core material can explain 20--40%. According to our results, sulfuric acid can explain the remainder of the growth, until the particle diameter is around 10--20 nm. After that secondary organic compounds significantly take part in growth process.