A new analytical expression has been derived to predict atmospheric conditions where homogeneous water-sulphuric acid nucleation will have a significant effect on aerosol and cloud condensation nuclei population. In the expression, the condensational sink due to pre-existing aerosol particles and source due to chemical production of sulphuric acid have been taken into account. The analytical expression has been derived using a sectional aerosol dynamic model including nucleation, condensation, coagulation, deposition and sulphuric acid formation in the gas phase. In the present study we have also compared the sectional model with modal and monodisperse models. All models may be used for predicting the onset of significant new particle formation. However, the computationally more efficient models-monodisperse, modal and sectional with low number of sections-over- or underpredict particle formation in some situations.