The differential $\mathrm{np}$ scattering cross section has been measured at 162 MeV in the angular range ${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}=72\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}180\ifmmode^\circ\else\textdegree\fi{}$, using the neutron beam facility at The Svedberg Laboratory in Uppsala. Special attention was paid to the absolute normalization of the data. In the angular range $150\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}180\ifmmode^\circ\else\textdegree\fi{}$, the data are steeper than those of most previous measurements and predictions from energy-dependent partial-wave analyses or nucleon-nucleon potentials. At $180\ifmmode^\circ\else\textdegree\fi{}$, the difference is of the order of 10\char21{}15%, an important change since this cross section is considered as a primary standard. It has also consequences for fundamental physics. Moreover, a value of the charged $\ensuremath{\pi}\mathrm{NN}$ coupling constant, ${g}_{{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}}^{2}=14.52\ifmmode\pm\else\textpm\fi{}0.26 {(f}_{{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}}^{2}=0.0803\ifmmode\pm\else\textpm\fi{}0.0014)$, is deduced from the data, using a novel extrapolation method. This is in good agreement with the classical text book value, but higher than those determined in recent partial-wave analyses of the nucleon-nucleon data base.