Mass and electrical charge are fundamental properties of biological macromolecules. Although molecular mass has long been determined with atomic precision, a direct and precise determination of molecular charge remains an outstanding challenge. Here we report high-precision (<1e) measurements of the electrical charge of molecules such as nucleic acids, and globular and disordered proteins in solution. The measurement is based on parallel external field-free trapping of single macromolecules, permits the estimation of a dielectric coefficient of the molecular interior and can be performed in real time. Further, we demonstrate the direct detection of single amino acid substitution and chemical modifications in proteins. As the electrical charge of a macromolecule strongly depends on its three-dimensional conformation, this kind of high-precision electrometry offers an approach to probe the structure, fluctuations and interactions of a single molecule in solution.