  Lattice QCD calculations of nucleon form factors are restricted to discrete
values of the Euclidean four-momentum transfer. Therefore, the extraction of
radii typically relies on parametrizing and fitting the lattice QCD data to
obtain its slope close to zero momentum transfer. We investigate a new method,
which allows to compute the nucleon radius directly from existing lattice QCD
data, without assuming a functional form for the momentum dependence of the
underlying form factor. The method is illustrated for the case of the isovector
mean square charge radius of the nucleon $\langle r^2_\mathrm{isov} \rangle$
and the quark-connected contributions to $\langle r^2_p\rangle$ and $\langle
r^2_n \rangle$ for the proton and neutron, respectively. Computations are
performed using a single gauge ensemble with $N_f=2+1+1$ maximally twisted mass
clover-improved fermions at physical quark mass and a lattice spacing of
$a=0.08\mathrm{fm}$.
