Spin relaxation of a single electron in a weakly coupled double quantum dot is calculated numerically. The phonon-assisted spin flip is allowed by the presence of the linear and cubic spin-orbit couplings and nuclear spins. The rate is calculated as a function of the interdot coupling, the magnetic field strength and orientation, and the dot bias. In an in-plane magnetic field, the rate is strongly anisotropic with respect to the magnetic field orientation, due to the anisotropy of the spin-orbit interactions. The nuclear spin influence is negligible. In an out-of-plane field, the nuclear spins play a more important role due selection rules imposed on the spin-orbit couplings. Our theory shows a very good agreement with data measured by Srinivasa et al. [Phys. Rev. Lett. 110, 196803 (2013)], allowing us to extract information on the linear spin-orbit interactions strengths in that experiment. We estimate that they correspond to spin-orbit lengths of about 5-15 mu m.