The neutron capture cross sections of and have been measured in the energy range from 3 to 225 keV at the Karlsruhe 3.75 MV Van de Graaff accelerator. Neutrons were produced via the reaction by bombarding metallic Li targets with a pulsed proton beam. The Karlsruhe barium fluoride detector was used for registration of capture events. The cross sections were determined relative to the gold standard using highly enriched metallic Cd samples. The respective ratios could be obtained with overall uncertainties between 0.8% and 1.6%, about an order of magnitude more accurate than previous data. Maxwellian averaged neutron capture cross sections were calculated for thermal energies between and 100 keV. Discrepancies of 30% to 40% were found with respect to previous data. The new cross sections provide a reliable definition of the s-abundance pattern of the Cd isotopes, thus improving the corresponding r-process residuals, and, most importantly, the impact of s-only as a normalization point for the overall distribution of the s abundances.