In this paper, we introduce a novel training method for making any monocular depth network learn absolute scale and estimate metric road-scene depth just from regular training data, i.e., driving videos. We refer to this training framework as StableCamH. The key idea is to leverage cars found on the road as sources of scale supervision but to incorporate them in the training robustly. StableCamH detects and estimates the sizes of cars in the frame and aggregates scale information extracted from them into a camera height estimate whose consistency across the entire video sequence is enforced as scale supervision. This realizes robust unsupervised training of any, otherwise scale-oblivious, monocular depth network to become not only scale-aware but also metric-accurate without the need for auxiliary sensors and extra supervision. Extensive experiments on the KITTI and Cityscapes datasets show the effectiveness of StableCamH and its state-of-the-art accuracy compared with related methods. We also show that StableCamH enables training on mixed datasets of different camera heights, which leads to larger-scale training and thus higher generalization. Metric depth reconstruction is essential in any road-scene visual modeling, and StableCamH democratizes its deployment by establishing the means to train any model as a metric depth estimator.