We present both experimental and theoretical investigations of the magnetic properties and electronic structure of the recently discovered superconductor W 7 Re 13 B. We determine the lower and the upper critical fields H c1 (0)=8.77mT and H c2 (0)=11.8T, which correspond to a penetration depth λ=2675Å and to a coherence length ξ=52Å. The Ginzburg–Landau parameter, κ is equal to 51. The effect of pressure on W 7 Re 13 B is negligible. This can be attributed to small changes in the density of states under pressure, or alternatively, to a low compressibility of this hard compound.