Concrete is the most widely manufactured material in the world. Its binding phase, calcium–silicate–hydrate (C–S–H), is responsible for its mechanical properties and has an atomic structure fairly similar to that of usual calcium silicate glasses, which makes it appealing to study this material with tools and theories traditionally used for non-crystalline solids. Here, following this idea, we use molecular dynamics simulations to evaluate the fracture toughness of C–S–H, inaccessible experimentally. This allows us to discuss the brittleness of the material at the atomic scale. We show that, at this scale, C–S–H breaks in a ductile way, which prevents one from using methods based on linear elastic fracture mechanics. Knowledge of the fracture properties of C–S–H at the atomic scale opens the way for an upscaling approach to the design of tougher cement paste, which would allow for the design of slender environment-friendly infrastructures, requiring less material.