Purpose: To calculate continuous breast density measures from processed images using deep learning. Method: Processed and unprocessed mammograms were collected for 3251 women attending the UK NHS Breast Screening Programme (NHSBSP). The breast density measures investigated included volumetric breast density, fibroglandular volume and breast volume. The ground truth for these measures was calculated using Volpara software on unprocessed mammograms. A deep learning model was trained and validated to predict each breast density measure. The performance of the deep learning model was assessed using a hold-out test set. Results: The breast volume and fibroglandular volume predicted with deep learning were strongly correlated with the ground truth (r=0.96 and r=0.88 respectively). The volumetric breast density had a Pearson correlation coefficient of 0.90. Conclusions: It is possible to predict volumetric breast density from processed images using deep learning.