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 m.