We investigate the thermodynamics of the anisotropic magnetic AdS5 black brane solution found by D’Hoker and Kraus. This solution is the gravity dual of a strongly coupled N=4 Super Yang-Mills plasma in ℝ3,1, with temperature T, in the presence of a magnetic field B. Following the procedure of holographic renormalisation we calculate the Gibbs free energy and the holographic stress tensor of the conformal plasma. We evaluate several thermodynamic quantities including the magnetisation, the anisotropic pressures and the speeds of sound. Our results are consistent with an RG flow from a perturbed AdS5 black brane at small B/T^2 to a BTZ×ℝ2 black brane at large B/T^2. We also perform a phenomenological analysis where we compare the thermodynamics of a magnetised conformal plasma against the lattice QCD results for the thermodynamics of the magnetised quark-gluon plasma.