The Avogadro constant, the number of entities in the amount of substance of one mole, links the atomic and the macroscopic properties of matter. Since the molar Planck constant is very well known via the measurement of the Rydberg constant, the Avogadro constant is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a new definition of the kilogram in terms of a fundamental constant. Here, we describe a new and unique approach for the determination of the Avogadro constant by “counting” the atoms in 1 kg single-crystal spheres, which are highly enriched with the ²⁸Si isotope. This approach has enabled us to apply isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, N_A=6.02214082(18)×10²³mol⁻¹, is now the most accurate input datum for a new definition of the kilogram.