We demonstrate quantitative phase mapping in confocal optical microscopy by applying synthetic optical holography (SOH), a recently introduced method for technically simple and fast phase imaging in scanning optical microscopy. SOH is implemented in a confocal microscope by simply adding a linearly moving reference mirror to the microscope setup, which generates a synthetic reference wave analogous to the plane reference wave of wide-field off-axis holography. We demonstrate that SOH confocal microscopy allows for non-contact surface profiling with sub-nanometer depth resolution. As an application for biological imaging, we apply SOH confocal microscopy to map the surface profile of an onion cell, revealing nanoscale-height features on the cell surface.