Cloud droplet formation depends on the condensation of water vapor on ambient aerosols, the rate of which is strongly affected by the kinetics of water uptake as expressed by the condensation (or mass accommodation) coefficient, αc. Estimates of αc for droplet growth from activation of ambient particles vary considerably and represent a critical source of uncertainty in estimates of global cloud droplet distributions and the aerosol indirect forcing of climate. We present an analysis of 10 globally relevant data sets of cloud condensation nuclei to constrain the value of αc for ambient aerosol. We find that rapid activation kinetics (αc > 0.1) is uniformly prevalent. This finding resolves a long-standing issue in cloud physics, as the uncertainty in water vapor accommodation on droplets is considerably less than previously thought.