The uncertainty evaluation of CSF2, the second caesium fountain primary frequency standard at PTB, is presented. The fountain uses optical molasses to cool atoms down to 0.6 μK. The atoms are launched vertically in a moving optical molasses, and state-selected in the |F = 3, m F = 0 hyperfine ground state. During their ballistic flight, the atoms interact twice with a microwave field, thus completing the Ramsey interaction. With a launch height of 36.5 cm above the cavity center, the central Ramsey fringe has a width of 0.9 Hz. About 3 × 10 4 atoms, 30% of the initial number in the |F = 3, m F = 0 state, are detected after their second interaction with the microwave field. Stabilizing the microwave frequency to the center of the central Ramsey fringe, a typical relative frequency instability of 2.5 × 10 −13 (τ /s) −1/2 is obtained. The CSF2 systematic uncertainty for realizing the SI second is estimated as 0.80 × 10 −15. First comparisons with the fountain CSF1 at the Physikalisch-Technische Bundesanstalt and other fountain frequency standards worldwide demonstrate agreement within the stated uncertainties.