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We present a generalised self-supervised learning approach for monocular estimation of the real depth across scenes with diverse depth ranges from 1--100s of meters. Existing supervised methods for monocular depth estimation require accurate depth measurements for training. This limitation has led to the introduction of self-supervised methods that are trained on stereo image pairs with a fixed camera baseline to estimate disparity which is transformed to depth given known calibration. Self-supervised approaches have demonstrated impressive results but do not generalise to scenes with different depth ranges or camera baselines. In this paper, we introduce RealMonoDepth a self-supervised monocular depth estimation approach which learns to estimate the real scene depth for a diverse range of indoor and outdoor scenes. A novel loss function with respect to the true scene depth based on relative depth scaling and warping is proposed. This allows self-supervised training of a single network with multiple data sets for scenes with diverse depth ranges from both stereo pair and in the wild moving camera data sets. A comprehensive performance evaluation across five benchmark data sets demonstrates that RealMonoDepth provides a single trained network which generalises depth estimation across indoor and outdoor scenes, consistently outperforming previous self-supervised approaches.