We present a combined analysis of the electromagnetic form factors of the nucleon in the space- and time-like regions using dispersion theory. Our framework provides a consistent description of the experimental data over the full range of momentum transfer, in line with the constraints from analyticity and unitarity. The statistical uncertainties of the extracted form factors are estimated using the bootstrap method, while systematic errors are determined from variations of the spectral functions. From the form factors, we determine precise values for the nucleon radii and comment on their puzzling status.