The regulation of size, volume and mass in living cells is physiologically important, and dysregulation of these parameters gives rise to many diseases. Cell mass is largely determined by the amount of water, proteins, lipids, carbohydrates and nucleic acids present in a cell, and is tightly linked to metabolism, proliferation and gene expression. Technologies have emerged in recent years that make it possible to track the masses of single suspended cells and adherent cells. However, it has not been possible to track individual adherent cells in physiological conditions at the mass and time resolutions required to observe fast cellular dynamics. Here we introduce a cell balance (a 'picobalance'), based on an optically excited microresonator, that measures the total mass of single or multiple adherent cells in culture conditions over days with millisecond time resolution and picogram mass sensitivity. Using our technique, we observe that the mass of living mammalian cells fluctuates intrinsically by around one to four per cent over timescales of seconds throughout the cell cycle. Perturbation experiments link these mass fluctuations to the basic cellular processes of ATP synthesis and water transport. Furthermore, we show that growth and cell cycle progression are arrested in cells infected with vaccinia virus, but mass fluctuations continue until cell death. Our measurements suggest that all living cells show fast and subtle mass fluctuations throughout the cell cycle. As our cell balance is easy to handle and compatible with fluorescence microscopy, we anticipate that our approach will contribute to the understanding of cell mass regulation in various cell states and across timescales, which is important in areas including physiology, cancer research, stem-cell differentiation and drug discovery.