Phase contrast mammography using a grating interferometer is an emerging technology for breast imaging. It provides complementary information to the conventional absorption-based methods. Additional diagnostic values could be further obtained by retrieving quantitative information from the three physical signals (absorption, differential phase and small-angle scattering) yielded simultaneously. We report a non-parametric quantitative volumetric breast density estimation method by exploiting the ratio (dubbed the R value) of the absorption signal to the small-angle scattering signal. The R value is used to determine breast composition and the volumetric breast density (VBD) of the whole breast is obtained analytically by deducing the relationship between the R value and the pixel-wise breast density. The proposed method is tested by a phantom study and a group of 27 mastectomy samples. In the clinical evaluation, the estimated VBD values from both cranio-caudal (CC) and anterior-posterior (AP) views are compared with the ACR scores given by radiologists to the pre-surgical mammograms. The results show that the estimated VBD results using the proposed method are consistent with the pre-surgical ACR scores, indicating the effectiveness of this method in breast density estimation. A positive correlation is found between the estimated VBD and the diagnostic ACR score for both the CC view (p = 0.033) and AP view (p = 0.001). A linear regression between the results of the CC view and AP view showed a correlation coefficient γ = 0.77, which indicates the robustness of the proposed method and the quantitative character of the additional information obtained with our approach.