Extracting geometric features from 3D scans or point clouds is the first step in many applications such as registration, reconstruction, and tracking. However, all state-of-the-art methods require either expensive low-level features as an input or patch-based feature extraction with limited receptive field size. In this work, we present fully-convolutional geometric features, low-dimensional metric features from a 3D fully-convolutional neural network for geometric correspondences. The proposed features are compact, capture large context through a fully-convolutional U-Net structure, and are scalable to large scenes. We experimentally validate our model on the standard registration datasets and show 39.4% reduction in error while being 27 times faster than the best learning-based method. In addition, the fully-convolutional geometric features are 16 times smaller (32-dimension) than the state-of-the-art method (512-dimension), making it an ideal candidate for fast registration.