  To date the magnetic radius of the proton has been determined only by means
of electron-proton scattering, which is not free of controversies. Any existing
atomic determinations are irrelevant because they are strongly model-dependent.
We consider a so-called Zemach contribution to the hyperfine interval in
ordinary and muonic hydrogen and derive a self-consistent model-independent
value of the magnetic radius of the proton. More accurately, we constrain not a
value of the magnetic radius by itself, but its certain combination with the
electric-charge radius of the proton, namely, R_E^2+R_M^2. The result from the
ordinary hydrogen is found to be R_E^2+R_M^2=1.35(12) fm^2, while the derived
muonic value is 1.49(18) fm^2. That allows us to constrain the value of the
magnetic radius of proton R_M=0.78(8) fm at the 10% level.
