The collision probability of cloud droplets in a turbulent flow has been investigated using direct numerical simulation. A novel simulation method is used in which synthetic turbulence is generated at the inlet and is transported through the flow domain with a mean carrier flow. For the dispersed phase a Lagrangian point particle model is applied. Collision statistics have been gathered for ten droplet sizes ranging from 5 to 50 µm in different statistic volumes in the turbulent flows with dissipation rates between 30 and 250 cm2 s-3 and Taylor-scale Reynolds numbers between 16.4 and 22.4. It is found that turbulence enhances the collision probability by factors up to 1.66 relative to gravitational settling. The resulting geometric collision kernel is decomposed into its primary contributions: the radial distribution function (RDF) and the mean radial relative velocity. The RDF quantifying the preferential droplet concentration reaches values up to 8.6, while a random distribution corresponds to 1. The mean radial relative velocity is enhanced by factors up to 1.18 relative to ravitational settling. The findings are in good quantitative agreement with results from other studies reported in the literature.