The Earth Clouds, Aerosols and Radiation Explorer (EarthCARE) satellite mission is a joint endeavour developed by the European Space Agency (ESA) and the Japan Aerospace Exploration Agency (JAXA) and features a 94 GHz Doppler Cloud Profiling Radar. This paper presents the theoretical basis of the cloud and precipitation microphysics (C-CLD) EarthCARE Level 2 (L2) algorithm. The C-CLD algorithm provides the best estimates of the vertical profiles of water mass content and hydrometeor characteristic size, obtained from radar reflectivity, path-integrated signal attenuation and hydrometeor sedimentation Doppler velocity estimates using optimal estimation (OE) theory. To obtain the forward model relations and the associated uncertainty, an ensemble-based method is used. This ensemble consists of a collection of in situ measured drop size distributions that cover natural microphysical variability. The ensemble mean and standard deviation represent the forward model relations and their microphysics-based uncertainty. The output variables are provided on the joint standard grid horizontal and EarthCARE Level 1b (L1b) vertical grid (1 km along track and 100 m vertically). The OE framework is not applied to liquid-only clouds in drizzle-free and lightly drizzling conditions, where a more statistical approach is preferred.