Based on the characteristics of secondary electron emission, the former formulae for the maximum yield of metals δm and primary range in the energy range of Wp0≤800 eV, relation L1 among secondary electron escape probability B, average energy required to produce an internal secondary electron 𝜀, δm, primary energy of δm (Wp0) and parameter R was deduced. On the basis of L1 and the former formula for δm, relation L2 among mean escape depth of secondary electrons emitted from metals 1/α, atomic number Z, back-scattering coefficient r, material density ρ, R, atomic weight Aα and Wp0 was deduced. According to the deduced L1, the formula for the ratio of B to 𝜀 and experimental ratio of δm to Wp0, relation L3 among R, original work function Φ and r were empirically obtained. According to the characteristics of metal surface, L1, L2 and L3, the formula for 1/α as a function of Z, r, ρ, Φ, Aα and Wp0 and that for δm as a function of r, Φ and Wp0 were deduced, respectively. The influences of surface change on 1/α and δm were analyzed. Calculated 1/α and δm were compared with the corresponding experimental ones. It was concluded that the deduced formulae for 1/α and δm can be used to estimate 1/α and δm, respectively.