Although essential for many cellular processes, the sequence of structural and molecular events during clathrin-mediated endocytosis remains elusive. While it was long believed that clathrin-coated pits grow with a constant curvature, it was recently suggested that clathrin first assembles to form flat structures that then bend while maintaining a constant surface area. Here, we combine correlative electron and light microscopy and mathematical growth laws to study the ultrastructural rearrangements of the clathrin coat during endocytosis in BSC-1 mammalian cells. We confirm that clathrin coats initially grow flat and demonstrate that curvature begins when around 70% of the final clathrin content is acquired. We find that this transition is marked by a change in the clathrin to clathrin-adaptor protein AP2 ratio and that membrane tension suppresses this transition. Our results support the notion that BSC-1 mammalian cells dynamically regulate the flat-to-curved transition in clathrin-mediated endocytosis by both biochemical and mechanical factors.