Organoids recapitulate complex 3D organ structures and represent a unique opportunity to probe the principles of self-organization. While we can alter an organoid’s morphology by manip- ulating the culture conditions, the morphology of an organoid often resembles that of its original organ, suggesting that organoid morphologies are governed by a set of tissue-specific constraints. Here, we establish a framework to identify constraints on an organoid’s morphological features by quantifying them from microscopy images of organoids exposed to a range of perturbations. We apply this framework to Madin-Darby Canine Kidney cysts and show that they obey a number of constraints taking the form of scaling relationships or caps on certain parameters. For example, we found that the number, but not size, of cells increases with increasing cyst size. We also find that these constraints vary with cyst age and can be altered by varying the culture conditions. This quan- titative framework for identifying constraints on organoid morphologies may inform future efforts to engineer organoids.