We demonstrate absolute quantitative mass density mapping in three dimensions of frozen-hydrated biological matter with an isotropic resolution of 180nm. As model for a biological system we use Chlamydomonas cells in buffer solution confined in a microcapillary. We use ptychographic X-ray computed tomography to image the entire specimen, including the 18μm-diameter capillary, thereby providing directly an absolute mass density measurement of biological matter with an uncertainty of about 6%. The resulting maps have sufficient contrast to distinguish cells from the surrounding ice and several organelles of different densities inside the cells. Organelles are identified by comparison with a stained, resin-embedded specimen, which can be compared with established transmission electron microscopy results. For some identified organelles, the knowledge of their elemental composition reduces the uncertainty of their mass density measurement down to 1% with values consistent with previous measurements of dry weight concentrations in thin cellular sections by scanning transmission electron microscopy. With prospects of improving the spatial resolution in the near future, we expect that the capability of non-destructive three-dimensional mapping of mass density in biological samples close to their native state becomes a valuable method for measuring the packing of organic matter on the nanoscale.