  We present a comprehensive study of the electromagnetic form factor, the
decay constant and the mass of the pion computed in lattice QCD with two
degenerate O(a)-improved Wilson quarks at three different lattice spacings in
the range 0.05-0.08fm and pion masses between 280 and 630MeV at m_pi L >~ 4.
Using partially twisted boundary conditions and stochastic estimators, we
obtain a dense set of precise data points for the form factor at very small
momentum transfers, allowing for a model-independent extraction of the charge
radius. Chiral Perturbation Theory (ChPT) augmented by terms which model
lattice artefacts is then compared to the data. At next-to-leading order the
effective theory fails to produce a consistent description of the full set of
pion observables but describes the data well when only the decay constant and
mass are considered. By contrast, using the next-to-next-to-leading order
expressions to perform global fits result in a consistent description of all
data. We obtain <r^2_pi>=0.481(33)(13)fm^2 as our final result for the charge
radius at the physical point. Our calculation also yields estimates for the
pion decay constant in the chiral limit, F_pi/F=1.080(16)(6), the quark
condensate, Sigma^{1/3}_MSbar(2GeV)=261(13)(1)MeV and several low-energy
constants of SU(2) ChPT.
