Breast density is a risk factor associated with the development of breast cancer. Usually, breast density is assessed on two dimensional (2D) mammograms using the American College of Radiology (ACR) classification. Magnetic resonance imaging (MRI) is a non-radiation based examination method, which offers a three dimensional (3D) alternative to classical 2D mammograms. We propose a new framework for automated breast density calculation on MRI data. Our framework consists of three steps. First, a recently developed method for simultaneous intensity inhomogeneity correction and breast tissue and parenchyma segmentation is applied. Second, the obtained breast component is extracted, and the breast-air and breast-body boundaries are refined. Finally, the fibroglandular/parenchymal tissue volume is extracted from the breast volume. The framework was tested on 37 randomly selected MR mammographies. All images were acquired on a 1.5T MR scanner using an axial, T1-weighted time-resolved angiography with stochastic trajectories sequence. The results were compared to manually obtained groundtruth. Dice's Similarity Coefficient (DSC) as well as Bland-Altman plots were used as the main tools for evaluation of similarity between automatic and manual segmentations. The average Dice's Similarity Coefficient values were 0.96±0.0172 and 0.83±0.0636 for breast and parenchymal volumes, respectively. Bland-Altman plots showed the mean bias (%) ± standard deviation equal 5.36±3.9 for breast volumes and -6.9±13.14 for parenchyma volumes. The automated framework produced sufficient results and has the potential to be applied for the analysis of breast volume and breast density of numerous data in clinical and research settings.