^{1}

^{1}

^{1}

^{2}

^{2}

^{1}

^{3}

^{3}

^{1}

^{4}

^{1}

^{3}

The formation rates of 3-nm particles were estimated at SMEAR IV, Puijo (Finland) where the continuous measurements extend only down to 7 nm in diameter. We extrapolated the formation rates at 7 nm (<i>J</i><sub>7</sub>) down to 3 nm (<i>J</i><sub>3</sub>) based on an approximate solution to the aerosol general dynamic equation, assuming a constant condensational growth rate, a power-law size dependent scavenging rate and negligible self-coagulation rate for the nucleation mode particles. To evaluate our method, we first applied it to new-particle formation (NPF) events in Hyytiälä (Finland), which extend down to 3 nm, and, therefore, <i>J</i><sub>3</sub> and <i>J</i><sub>7</sub> can be determined directly from the measured size distribution evolution. The Hyytiälä results show that the estimated daily mean <i>J</i><sub>3</sub> slightly overestimate the observed mean <i>J</i><sub>3</sub>, but a promising 84 % of the estimated <i>J</i><sub>3</sub> are within a factor of 2 from the measured ones. However, when considering detailed daily time evolution, the agreement is typically poor presumably due to uncertainties in estimated growth rates which are required in order to calculate the time-lag between formation of 3-nm and 7-nm particles. At Puijo, the mean and median <i>J</i><sub>7</sub> for clear NPF days during April 2007–December 2015 were 0.23 and 0.07 cm<sup>−3</sup> s<sup>−1</sup>, respectively, while the extrapolated mean and median <i>J</i><sub>3</sub> were 0.47 and 0.13 cm<sup>−3</sup> s<sup>−1</sup>, respectively.