Abstract At low four-momentum transfer squared $0.02 < -t < 0.2$ (GeV/$c$)$^{2}$, we use the Chou–Yang model to predict the form factor of protons from proton–proton elastic scattering at center-of-mass energy $\sqrt s=8$ TeV. By fitting differential cross-sectional data from the TOTEM experiment to a single Gaussian, the form factor is extracted. We use this form factor to find the rms matter radius of the proton to be 0.88 fm, which is in good agreement with the experimental data and the theoretically predicted values of the rms radius.