Fundamental questions remain about the origin of newly formed atmospheric aerosol particles because data from laboratory measurements have been insufficient to build global models. In contrast, gas-phase chemistry models have been based on laboratory kinetics measurements for decades. We built a global model of aerosol formation by using extensive laboratory measurements of rates of nucleation involving sulfuric acid, ammonia, ions, and organic compounds conducted in the CERN CLOUD (Cosmics Leaving Outdoor Droplets) chamber. The simulations and a comparison with atmospheric observations show that nearly all nucleation throughout the present-day atmosphere involves ammonia or biogenic organic compounds, in addition to sulfuric acid. A considerable fraction of nucleation involves ions, but the relatively weak dependence on ion concentrations indicates that for the processes studied, variations in cosmic ray intensity do not appreciably affect climate through nucleation in the present-day atmosphere.