We study a model-independent parametrization of the vector pion form factor that arises from the constraints of analyticity and unitarity. Our description should be suitable up to $\sqrt{s}\ensuremath{\simeq}1.2 \mathrm{GeV}$ and allows a model-independent determination of the mass of the $\ensuremath{\rho}(770)$ resonance, ${M}_{\ensuremath{\rho}}=(775.1\ifmmode\pm\else\textpm\fi{}0.5) \mathrm{MeV}.$ We analyze the experimental data on ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ in this framework, and its consequences on the low-energy observables worked out by chiral perturbation theory. An evaluation of the two pion contribution to the anomalous magnetic moment of the muon, ${a}_{\ensuremath{\mu}},$ and to the fine structure constant, $\ensuremath{\alpha}{(M}_{Z}^{2}),$ is also performed.