The quest for the value of the electron's atomic mass has been the subject of continuing efforts over the past few decades. Among the seemingly fundamental constants that parameterize the Standard Model of physics and which are thus responsible for its predictive power, the electron mass me is prominent, being responsible for the structure and properties of atoms and molecules. It is closely linked to other fundamental constants, such as the Rydberg constant R∞ and the fine-structure constant α (ref. 6). However, the low mass of the electron considerably complicates its precise determination. Here we combine a very precise measurement of the magnetic moment of a single electron bound to a carbon nucleus with a state-of-the-art calculation in the framework of bound-state quantum electrodynamics. The precision of the resulting value for the atomic mass of the electron surpasses the current literature value of the Committee on Data for Science and Technology (CODATA) by a factor of 13. This result lays the foundation for future fundamental physics experiments and precision tests of the Standard Model.