Context : Aims : We aim for an understanding of the morphological and spectral properties of the supernova remnant RCW 86 and for insights into the production mechanism leading to the RCW 86 very high-energy \gamma -ray emission . Methods : We analyzed High Energy Spectroscopic System ( H.E.S.S . ) data that had increased sensitivity compared to the observations presented in the RCW 86 H.E.S.S . discovery publication . Studies of the morphological correlation between the 0.5 – 1 keV X-ray band , the 2 – 5 keV X-ray band , radio , and \gamma -ray emissions have been performed as well as broadband modeling of the spectral energy distribution with two different emission models . Results : We present the first conclusive evidence that the TeV \gamma -ray emission region is shell-like based on our morphological studies . The comparison with 2 – 5 keV X-ray data reveals a correlation with the 0.4 – 50 TeV \gamma -ray emission . The spectrum of RCW 86 is best described by a power law with an exponential cutoff at E _ { cut } = ( 3.5 \pm 1.2 _ { stat } ) \mathrm { TeV } and a spectral index of \Gamma \approx 1.6 \pm 0.2 . A static leptonic one-zone model adequately describes the measured spectral energy distribution of RCW 86 , with the resultant total kinetic energy of the electrons above 1 \mathrm { GeV } being equivalent to \sim 0.1 % of the initial kinetic energy of a Type I a supernova explosion ( 10 ^ { 51 } \mathrm { erg } ) . When using a hadronic model , a magnetic field of B \approx 100 \mu \mathrm { G } is needed to represent the measured data . Although this is comparable to formerly published estimates , a standard E ^ { -2 } spectrum for the proton distribution can not describe the \gamma -ray data . Instead , a spectral index of \Gamma _ { p } \approx 1.7 would be required , which implies that \sim 7 \times 10 ^ { 49 } / n _ { \mathrm { cm } ^ { -3 } } \mathrm { erg } has been transferred into high-energy protons with the effective density n _ { \mathrm { cm } ^ { -3 } } = n / 1 \mathrm { cm } ^ { -3 } . This is about 10 % of the kinetic energy of a typical Type Ia supernova under the assumption of a density of 1 cm ^ { -3 } . Conclusions :