The fine balance of growth and division is a fundamental property of the physiology of cells, and one of the least understood. Its study has been thwarted by difficulties in the accurate measurement of cell size and the even greater challenges of measuring growth of a single cell over time. We address these limitations by demonstrating a computationally enhanced methodology for quantitative phase microscopy for adherent cells, using improved image processing algorithms and automated cell-tracking software. Accuracy has been improved more than twofold and this improvement is sufficient to establish the dynamics of cell growth and adherence to simple growth laws. It is also sufficient to reveal unknown features of cell growth, previously unmeasurable. With these methodological and analytical improvements, in several cell lines we document a remarkable oscillation in growth rate, occurring throughout the cell cycle, coupled to cell division or birth yet independent of cell cycle progression. We expect that further exploration with this advanced tool will provide a better understanding of growth rate regulation in mammalian cells.