An analytical expression for the critical radius associated with Kessler-type parameterizations of the autoconversion process is derived. The expression can be used to predict the critical radius from the cloud liquid water content and the droplet number concentration, eliminating the need to prescribe the critical radius as an empirical constant in numerical models. Data from stratiform clouds are analyzed, indicating that on average continental clouds have larger critical radii than maritime clouds. This work further suggests that anthropogenic aerosols affect the autoconversion process by increasing the critical radius and decreasing the characteristic radius, which in turn inhibits the initiation of embryonic raindrops, and by decreasing the autoconversion rate after the initiation process. The potential impact of this work on the evaluation of the second indirect aerosol effect is discussed.