Based on the range–energy relationship, the characteristics of secondary electron emission, some relationship between the secondary electron yield δ and experimental results, the universal formulae for δ0.8−2 (the subscript indicates that the energy range of primary energy at the surface Wpo is from 0.8 keV to 2 keV) and δ2−10 for metals were deduced. The δ0.8−10 calculated with the universal formulae and the δ0.8−10 measured experimentally were compared, and the scattering of δ for the same metal was analysed. Finally, we concluded that the formulae were universal for δ0.8−10 for metals. On the basis of some relationship between parameters of δ, we deduce a formula for expressing total stopping power S0.8−10 as a function of S10−30, δ0.8−10, δ10−30, backscattered coefficient η0.8−10, η10−30 and Wpo. The calculated S0.8−10 were compared with the values measured experimentally and it was concluded that the formula to estimate S0.8−10 was universal for metals.