X-ray phase-contrast imaging is a novel technology that achieves high soft-tissue contrast. Although its clinical impact is still under investigation, the technique may potentially improve clinical diagnostics. In conventional attenuation-based X-ray computed tomography, radiological diagnostics are quantified by Hounsfield units. Corresponding Hounsfield units for phase-contrast imaging have been recently introduced, enabling a setup-independent comparison and standardized interpretation of imaging results. Thus far, the experimental values of few tissue types have been reported;these values have been determined from fixated tissue samples. This study presents phase-contrast Hounsfield units for various types of non-fixated human soft tissues. A large variety of tissue specimens ranging from adipose, muscle and connective tissues to liver, kidney and pancreas tissues were imaged by a grating interferometer with a rotating-anode X-ray tube and a photon-counting detector. Furthermore, we investigated the effects of formalin fixation on the quantitative phase-contrast imaging results.