Homogeneous ternary nucleation rates of water, ammonia (NH3), and inorganic acids are calculated from classical nucleation theory at various combinations of temperature and ambient vapor concentrations. Mixtures with sulfuric acid (H2SO4), nitric acid (HNO3), hydrochloric acid (HCl), and methane sulfonic acid (CH3SO3H or MSA) are considered. The results are compared to assess the relative importance of different nucleation routes. Vapors with an acid and an alkaline (ammonia) component are shown to nucleate more readily than vapors having two acid species. Much lower concentrations of H2SO4 than HNO3 or HCl are required to reach the same nucleation rate at similar vapor concentrations of H2O and NH3. Nucleation rates in H2O-H2SO4-HNO3 and H2O-H2SO4-MSA vapors are close to the limit of H2O-H2SO4 nucleation, even at high concentrations of MSA and HNO3. The results suggest that H2O-H2SO4-NH3 nucleation is the foremost ternary nucleation route in the atmosphere.