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Glomerulosclerosis, interstitial fibrosis, and tubular atrophy (IFTA) are histologic indicators of irrecoverable kidney injury. In standard clinical practice, the renal pathologist visually assesses, under the microscope, the percentage of sclerotic glomeruli and the percentage of renal cortical involvement by IFTA. Estimation of IFTA is a subjective process due to a varied spectrum and definition of morphological manifestations. Modern artificial intelligence and computer vision algorithms have the ability to reduce inter-observer variability through rigorous quantitation. In this work, we apply convolutional neural networks for the segmentation of glomerulosclerosis and IFTA in periodic acid-Schiff stained renal biopsies. The convolutional network approach achieves high performance in intra-institutional holdout data, and achieves moderate performance in inter-intuitional holdout data, which the network had never seen in training. The convolutional approach demonstrated interesting properties, such as learning to predict regions better than the provided ground truth as well as developing its own conceptualization of segmental sclerosis. Subsequent estimations of IFTA and glomerulosclerosis percentages showed high correlation with ground truth.