  Few unified equations of state for neutron star matter where core and crust
are described using the same nuclear model are available. However the use of
non-unified equations of state with a simplified matching between the crust and
the core has been shown to introduce uncertainties in the radius determination
which can be larger than the expected precision of the next generation of X-ray
satellites.
  We aim at eliminating the dependence of the radius and mass of neutron staron
the detailed model for the crust and on the crust-core matching procedure. We
solve the approximate equations of the hydrostatic equilibrium for the crust of
neutron stars obtaining a precise formula for the radius which depends only on
the core mass and radius, and on the baryon chemical potential at the
core-crust interface and on the crust surface. For a fully accreted crust one
needs additionally the value of the total deep crustal heating per one accreted
nucleon.
  For typical neutron star masses the approximate approach allows to determine
the neutron star radius with an error ~0.1% (~ 10 m, equivalent to a 1%
inaccuracy in the crust thickness).
  The formalism applies to neutron stars with a catalyzed or a fully accreted
crust. The difference in the neutron star radius between the two models is
proportional to the total energy release due to deep crustal heating.
  For a given model of dense matter describing the neutron star core, the
radius of a neutron star can be accurately determined independently of the
crust model with a precision much better than the ~5% one expected from the
next generation of X-ray satellites. This allows to circumvent the problem of
the radius uncertainty which may arise when non-unified equations of state for
the crust and the core are used.
