  We study polarisation of W-bosons produced in association with one jet at the
LHC. In particular, we provide all necessary theoretical ingredients for the
precise extraction of polarisation fractions. To that end, we present new
polarised predictions up to NNLO QCD accuracy employing the narrow-width
approximation, in two phase spaces: inclusive and fiducial. We compare results
in the fiducial phase space to a full off-shell computation as well as
experimental data. Finally, we fit the polarisation fractions using shape
templates and show that NNLO corrections significantly improve their
determination.
