Reconstruction of shapes and sizes of three-dimensional (3D) objects from two- dimensional (2D) information is an intensely studied subject in computer vision. We here consider the level of single cells and nuclei and present a neural network-based SHApe PRediction autoencoder. For proof-of-concept, SHAPR reconstructs 3D shapes of red blood cells from single view 2D confocal microscopy images more accurately than naïve stereological models and significantly increases the feature-based prediction of red blood cell types from F1 = 79% to F1 = 87.4%. Applied to 2D images containing spheroidal aggregates of densely grown human induced pluripotent stem cells, we find that SHAPR learns fundamental shape properties of cell nuclei and allows for prediction-based morphometry. Reducing imaging time and data storage, SHAPR will help to optimize and up-scale image-based high-throughput applications for biomedicine.