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

Model-independent determination of the magnetic radius of the proton from spectroscopy of ordinary and muonic hydrogen