The ratio of the nuclear binding energy to the charge radius is systematically analyzed based on the experimental data of both. The linear relationship is observed between the ratios for nuclei $(Z,N)$ and those for $(Z,N-2)$. Together with this linear relationship, the nuclear charge radius can be extracted based on the radial basis function approach. The root-mean-square (rms) deviation with respect to 1063 measured nuclear charge radii reaches 0.007 fm, and the rms deviation of the test set for the neutron-rich region is 0.014 fm. The charge radii for 1333 nuclei are extracted, including 270 unmeasured nuclei. The new probe indicates that large deformations occur in atomic nuclei starting from neutron number $N=89$ in the isotope chains with proton numbers $Z=63$ and 65, based on the analysis of nuclear binding energy and charge radius. The proposed method enables charge-radius extraction from binding-energy data alone, providing a new approach for nuclei with unmeasurable charge radii.

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• Binding energy & masses
• Nuclear charge distribution
• Nuclear charge radii
• Nuclear radii
• Nuclear structure & decays
• Machine learning