The modelling of emission spectra of molecules seen in interstellar clouds requires the knowledge of collisional rate coefficients. Among the commonly observed species, N 2 H + is of particular interest since it was shown to be a good probe of the physical conditions of cold molecular clouds. Thus, we have calculated hyperfine-structure resolved excitation rate coefficients of N 2 H + (X 1 Σ + ) by H 2 (j = 0), the most abundant collisional partner in the cold interstellar medium. The calculations are based on a new potential energy surface, obtained from highly correlated ab initio calculations. State-to-state rate coefficients between the first hyperfine levels were calculated, for temperatures ranging from 5 K to 70 K. By comparison with previously published N 2 H + -He rate coefficients, we found significant differences which cannot be reproduced by a simple scaling relationship. As a first application, we also performed radiative transfer calculations, for physical conditions typical of cold molecular clouds. We found that the simulated line intensities significantly increase when using the new H 2 rate coefficients, by comparison with the predictions based on the He rate coefficients. In particular, we revisited the modelling of the N 2 H + emission in the LDN 183 core, using the new collisional data, and found that all three of the density, gas kinetic temperature and N 2 H + abundance had to be revised.