We present the proton and neutron vector form factors in a convenient parametric form that is optimized for momentum transfers ≲ few GeV 2. The form factors are determined from a global fit to electron scattering data and precise charge radius measurements. A new treatment of radiative corrections is applied. This parametric representation of the form factors, uncertainties, and correlations provides an efficient means to evaluate many derived observables. We consider two classes of illustrative examples: neutrinonucleon scattering cross sections at GeV energies for neutrino oscillation experiments and nucleon structure corrections for atomic spectroscopy. The neutrino-nucleon charged current quasielastic cross section differs by 3%-5% compared to commonly used form factor models when the vector form factors are constrained by recent high-statistics electron-proton scattering data from the A1 Collaboration. Nucleon structure parameter determinations include: the magnetic and Zemach radii of the proton and neutron, ½r p M ; r n M ¼ ½0.739ð41Þð23Þ; 0.776ð53Þð28Þ fm and ½r p Z ; r n Z ¼ ½1.0227ð94Þð51Þ; −0.0445ð14Þð3Þ fm; the Friar radius of nucleons, ½ðr p F Þ 3 ; ðr n F Þ 3 ¼ ½2.246ð58Þð2Þ; 0.0093ð6Þð1Þ fm 3 ; the electric curvatures, ½hr 4 i p E ; hr 4 i n E ¼ ½1.08ð28Þð5Þ; −0.33ð24Þð3Þ fm 4 ; and bounds on the magnetic curvatures, ½hr 4 i p M ; hr 4 i n M ¼ ½−2.0ð1.7Þð0.8Þ; −2.3ð2.1Þð1.1Þ fm 4. The first and dominant uncertainty is propagated from the experimental data and radiative corrections, and the second error is due to the fitting procedure.