In the literature it was recently reported that for hypersonic reactive flow the shock stand-off distance depends not only on a reaction rate parameter, but also on the density ratio between shock and body. This is confirmed in this paper by a theoretical approach which is based on the governing conservation equations. Reasonable simplifications are introduced which for the frozen and equilibrium case allow an analytical solution for the stand-off distance on spheres. The solution method is restricted to this area since only the stand-off distance at the stagnation point is of interest. The excellent agreement achieved for the frozen or non-reactive case with well-known solutions gives evidence for the correctness of the solution method. For the equilibrium case the solution obtained shows the same behaviour as a recent study which agrees with experimental results and numerical simulations.