Abstract <p>Perfect edges are essential for next-generation electronics based on two-dimensional (2D) materials, yet achieving atomic smoothness remains elusive. Here, we establish the physical limits of edge roughness through molecular dynamics simulations empowered by chemically accurate machine learning force fields. In graphene, we demonstrate that pristine armchair and zigzag edges emerge through precisely controlled mechanical cleavage, while misalignment beyond a threshold creates kinked patterns following crystallographic directions. A fracture mechanics analysis reveals how the interplay between kinetic and dynamic effects governs crack paths and edge morphology. This understanding extends to more complex 2D materials, from crystalline bilayer silica where symmetry breaking drives unique cleavage behavior to amorphous silica where topological disorder fundamentally alters the edge-loading relationship. Our findings not only establish the theoretical bounds of edge smoothness, but also provide practical strategies for engineering atomically precise edges crucial for quantum devices and nanoelectronics.</p> Impact statement <p>Surface and edge roughness are critical factors determining material performance, impacting applications from tribology to quantum electronics. Achieving atomic-scale smoothness is crucial for realizing advanced technologies. Our study, leveraging molecular dynamics simulations, unravels the underlying physics governing edge roughness in two-dimensional materials. By controlling loading conditions and minimizing dynamic effects, we demonstrate the possibility of achieving ultraflat or even atomically smooth edges. These insights offer a roadmap for the fabrication of high-performance materials with precise control over surface and edge properties.</p> Graphical abstract <p></p>