If it were straightened out, the DNA of viruses would be on the order of millimeters long, while the DNA of human beings would be on the order of meters. Clearly cells and viruses are much smaller than this -- on the order of microns (or less) -- and the space that DNA occupies in a cell or virus is yet smaller! Much like tidying up your room, packing DNA requires energy...but what amount of energy is needed to bring DNA "down to size"?

[DNA packing in bacteriophage Phi 29. Image courtesy of LR Commoli, et al.]