Based on the range–energy relationship, the characteristics of secondary electron emission, some relationship between the secondary electron yield $\delta$ and experimental results, the universal formulae for $\delta_{0.8−2}$ (the subscript indicates that the energy range of primary energy atthe surface W$_{\rm po}$ is from 0.8 keV to 2 keV) and $\delta_{2−10}$ for metals were deduced. The $\delta_{0.8−10}$ calculated with the universal formulae and the$\delta_{0.8−10}$ measured experimentally were compared, and the scattering of $\delta$ for the same metal was analysed. Finally, we concluded that the formulae were universal for $\delta_{0.8−10}$ for metals. On the basis of some relationship between parameters of $\delta$, wededuce a formula for expressing total stopping power $S_{0.8−10}$ as a function of $S_{10−30}, \delta_{0.8−10}, \delta_{10−30}$, backscattered coefficient $\heta_{0.8−10}, \heta_{10−30}$ and W$_{\rm po}. The calculated $S_{0.8−10}$ were compared with the values measured experimentally and it was concluded that the formula to estimate $S_{0.8−10}$ was universal for metals.