  The current status of the determination of corrections to the hyperfine
splitting of the ground state in hydrogen is considered. Improved calculations
are provided taking into account the most recent value for the proton charge
radius. Comparing experimental data with predictions for the hyperfine
splitting, the Zemach radius of the proton is deduced to be $1.045(16)$ fm.
Employing exponential parametrizations for the electromagnetic form factors we
determine the magnetic radius of the proton to be $0.778(29)$ fm. Both values
are compared with the corresponding ones derived from the data obtained in
electron-proton scattering experiments and the data extracted from a rescaled
difference between the hyperfine splittings in hydrogen and muonium.
