Balancing the rate of differentiation and proliferation in developing tissues is essential to produce organs of robust size and composition. Although many molecular regulators have been established, how these connect to physical and geometrical aspects of tissue architecture is poorly understood. Here, using high-resolution timelapse imaging, we find that changes to cell geometry associated with dense tissue packing play a significant role in regulating differentiation rate in the zebrafish neural tube. Specifically, progenitors that are displaced away from the apical surface due to crowding, tend to differentiate in a Notch-dependent manner. Using simulations we show that interplay between progenitor density, cell shape and changes in differentiation rate could naturally result in negative-feedback control on progenitor cell number. Given these results, we suggest a model whereby differentiation rate is regulated by density dependent effects on cell geometry to: (1) correct variability in cell number; and (2) balance the rates of proliferation and differentiation over development to 'fill' the available space.