  We present data for the axial coupling constant g_A of the nucleon obtained
in lattice QCD with two degenerate flavours of dynamical non-perturbatively
improved Wilson quarks. The renormalisation is also performed
non-perturbatively. For the analysis we give a chiral extrapolation formula for
g_A based on the small scale expansion scheme of chiral effective field theory
for two degenerate quark flavours. Applying this formalism in a finite volume
we derive a formula that allows us to extrapolate our data simultaneously to
the infinite volume and to the chiral limit. Using the additional lattice data
in finite volume we are able to determine the axial coupling of the nucleon in
the chiral limit without imposing the known value at the physical point.
