Context. Solar magnetic fields are regularly extrapolated into the corona starting from photospheric magnetic measurements that can be affected by significant uncertainty. Aims: We study how inaccuracies introduced into the maps of the photospheric magnetic vector by the inversion of ideal and noisy Stokes parameters influence the extrapolation of nonlinear force-free magnetic fields. Methods: We compute nonlinear force-free magnetic fields based on simulated vector magnetograms, by the inversion of Stokes profiles that were computed by a 3-D radiation MHD simulation snapshot. These extrapolations are compared with extrapolations that originate directly in the field in the MHD simulations, which is our reference. We investigate how line formation and instrumental effects such as noise, limited spatial resolution, and the effect of employing a filter instrument influence the resulting magnetic field structure. The comparison is performed qualitatively by visually inspecting the magnetic field distribution and quantitatively by different metrics. Results: The reconstructed field is most accurate if ideal Stokes data are inverted and becomes less accurate if instrumental effects and noise are included. The results demonstrate that the nonlinear force-free field extrapolation method tested here is relatively insensitive to the effects of noise in measured polarization spectra at levels consistent with present-day instruments. Conclusions: Our results show that we can reconstruct the coronal magnetic field as a nonlinear force-free field from realistic photospheric measurements with an accuracy of a few percent, at least in the absence of sunspots.