A new fast clear-sky model called McClear was developed to estimate the downwelling shortwave direct and global irradiances received at ground level under clear skies. It is a fully physical model replacing empirical relations or simpler models used before. It exploits the recent results on aerosol properties, and total column content in water vapour and ozone produced by the MACC project (Monitoring Atmosphere Composition and Climate). It accurately reproduces the irradiance computed by the libRadtran reference radiative transfer model with a computational speed approximately 10<sup>5</sup> times greater by adopting the abaci, or look-up table, approach combined with interpolation functions. It is therefore suited for geostationary satellite retrievals or numerical weather prediction schemes with many pixels or grid points, respectively. McClear irradiances were compared to 1 min measurements made in clear-sky conditions at several stations within the Baseline Surface Radiation Network in various climates. The bias for global irradiance comprises between −6 and 25 W m<sup>−2</sup>. The RMSE ranges from 20 W m<sup>−2</sup> (3% of the mean observed irradiance) to 36 W m<sup>−2</sup> (5%) and the correlation coefficient ranges between 0.95 and 0.99. The bias for the direct irradiance comprises between −48 and +33 W m<sup>−2</sup>. The root mean square error (RMSE) ranges from 33 W m<sup>−2</sup> (5%) to 64 W m<sup>−2</sup> (10%). The correlation coefficient ranges between 0.84 and 0.98. This work demonstrates the quality of the McClear model combined with MACC products, and indirectly the quality of the aerosol properties modelled by the MACC reanalysis.