This paper presents a measurement of the polarisation of τ leptons produced in Z/γ∗→ττ decays which is performed with a dataset of proton—proton collisions at s=8 TeV, corresponding to an integrated luminosity of 20.2 fb -1 recorded with the ATLAS detector at the LHC in 2012. The Z/γ∗→ττ decays are reconstructed from a hadronically decaying τ lepton with a single charged particle in the final state, accompanied by a τ lepton that decays leptonically. The τ polarisation is inferred from the relative fraction of energy carried by charged and neutral hadrons in the hadronic τ decays. The polarisation is measured in a fiducial region that corresponds to the kinematic region accessible to this analysis. The τ polarisation extracted over the full phase space within the Z/γ∗ mass range of 66