We present a new parametrization of the cosmic-ray flux and its mass composition over an energy range from 10 GeV to $10^{11}$ GeV. Our approach is data-driven and relies on theoretical assumptions as little as possible. We combine measurements of the flux of individual elements from high-precision satellites and balloon experiments with indirect measurements of mass groups from the leading air shower experiments. To our knowledge, we provide the first fit of this kind that consistently takes both statistical and systematic uncertainties into account. The uncertainty on the energy scales of individual experiments is handled explicitly in our mathematical approach. Part of our results is a common energy scale and adjustment factors for the energy scales of the participating experiments. Our fit has a reduced $\chi^2$-value of 0.5, showing that experimental data are in good agreement, if systematic uncertainties are considered. Our model may serve as a world-average of the measured fluxes for individual elements from proton to iron from 10 GeV to $10^{11}$ GeV. It is useful as an input for simulations or theoretical computations based on cosmic rays. The experimental uncertainties of the input data are captured in a covariance matrix, which can be propagated into derived quantities.