The ability to quantify structural changes of the endoplasmic reticulum (ER) is crucial for understanding the structure and function of this organelle. However, the rapid movement and complex topology of ER networks make this challenging. Here, we construct a state-of-the-art semantic segmentation method that we call ERnet for the automatic classification of sheet and tubular ER domains inside individual cells. Data are skeletonized and represented by connectivity graphs, enabling precise and efficient quantification of network connectivity. ERnet generates metrics on topology and integrity of ER structures and quantifies structural change in response to genetic or metabolic manipulation. We validate ERnet using data obtained by various ER-imaging methods from different cell types as well as ground truth images of synthetic ER structures. ERnet can be deployed in an automatic high-throughput and unbiased fashion and identifies subtle changes in ER phenotypes that may inform on disease progression and response to therapy.