X-ray free-electron lasers (XFELs) open the possibility of obtaining diffraction information from a single biological macromolecule. This is because XFELs can generate extremely intense x-ray pulses that are so short that diffraction data can be collected before the sample is destroyed. By collecting a sufficient number of single-particle diffraction patterns, the three-dimensional electron density of a molecule can be reconstructed ab initio. The quality of the reconstruction depends largely on the number of patterns collected at the experiment. This paper provides an estimate of the number of diffraction patterns required to reconstruct the electron density at a targeted spatial resolution. This estimate is verified by simulations for realistic x-ray fluences, repetition rates, and experimental conditions available at modern XFELs. Employing the bacterial phytochrome as a model system, we demonstrate that sub-nanometer resolution is within reach.