The formation of particles from precursor vapors is an important source of atmospheric aerosol. Research at the Cosmics Leaving OUtdoor Droplets (CLOUD) facility at CERN tries to elucidate which vapors are responsible for this new-particle formation, and how in detail it proceeds. Initial measurement campaigns at the CLOUD stainless-steel aerosol chamber focused on investigating particle formation from ammonia (NH sub(3)) and sulfuric acid (H sub(2)SO sub(4)). Experiments were conducted in the presence of water, ozone and sulfur dioxide. Contaminant trace gases were suppressed at the technological limit. For this study, we mapped out the compositions of small NH sub(3)-H sub(2)SO sub(4) clusters over a wide range of atmospherically relevant environmental conditions. We covered NH sub(3) in the range from < 2 to 1400 pptv, H sub(2)SO sub(4) from 3.3 x 10 super(6) to 1.4 x 10 super(9) cm super(-3) (0.1 to 56 pptv), and a temperature range from -25 to +20 degree C. Negatively and positively charged clusters were directly measured by an atmospheric pressure interface time-of-flight (APi-TOF) mass spectrometer, as they initially formed from gas-phase NH sub(3) and H sub(2)SO sub(4), and then grew to larger clusters containing more than 50 molecules of NH sub(3) and H sub(2)SO sub(4), corresponding to mobility-equivalent diameters greater than 2 nm. Water molecules evaporate from these clusters during sampling and are not observed. We found that the composition of the NH sub(3)-H sub(2)SO sub(4) clusters is primarily determined by the ratio of gas-phase concentrations NH sub(3) / H sub(2)SO sub(4), as well as by temperature. Pure binary H sub(2)O-H sub(2)SO sub(4) clusters (observed as clusters of only H sub(2)SO sub(4)) only form at NH sub(3) / H sub(2)SO sub(4) < 0.1 to 1. For larger values of NH sub(3) / H sub(2)SO sub(4), the composition of NH sub(3)-H sub(2)SO sub(4) clusters was characterized by the number of NH sub(3) molecules m added for each added H sub(2)SO sub(4) molecule n ( Delta m/ Delta n), where n is in the range 4-18 (negatively charged clusters) or 1-17 (positively charged clusters). For negatively charged clusters, Delta m/ Delta n saturated between 1 and 1.4 for NH sub(3) / H sub(2)SO sub(4) > 10. Positively charged clusters grew on average by Delta m/ Delta n = 1.05 and were only observed at sufficiently high NH sub(3) / H sub(2)SO sub(4). The H sub(2)SO sub(4) molecules of these clusters are partially neutralized by NH sub(3), in close resemblance to the acid-base bindings of ammonium bisulfate. Supported by model simulations, we substantiate previous evidence for acid-base reactions being the essential mechanism behind the formation of these clusters under atmospheric conditions and up to sizes of at least 2 nm. Our results also suggest that electrically neutral NH sub(3)-H sub(2)SO sub(4) clusters, unobservable in this study, have generally the same composition as ionic clusters for NH sub(3) / H sub(2)SO sub(4) > 10. We expect that NH sub(3)-H sub(2)SO sub(4) clusters form and grow also mostly by Delta m/ Delta n > 1 in the atmosphere's boundary layer, as NH sub(3) / H sub(2)SO sub(4) is mostly larger than 10. We compared our results from CLOUD with APi-TOF measurements of NH sub(3)-H sub(2)SO sub(4) anion clusters during new-particle formation in the Finnish boreal forest. However, the exact role of NH sub(3)-H sub(2)SO sub(4) clusters in boundary layer particle formation remains to be resolved.