Nitrogen-vacancy (NV) defect centers in diamond are promising solid-state magnetometers. Single centers allow for high-spatial-resolution field imaging but are limited in their magnetic field sensitivity. Using defect-center ensembles, sensitivity can be scaled with N when N is the number of defects. In the present work, we use an ensemble of N∼1011 defect centers within an effective sensor volume of 8.5×10−4mm3 for sensing at room temperature. By carefully eliminating noise sources and using high-quality diamonds with large NV concentrations, we demonstrate, for such sensors, a sensitivity scaling as 1/t , where t is the total measurement time. The associated photon-shot-noise-limited magnetic-field sensitivity for ac signals of f=20kHz is 0.9pT/Hz . For a total measurement time of 100 s, we reach a standard deviation of about 100 fT. Further improvements using decoupling sequences and material optimization could lead to fT/Hz sensitivity.