Based on the processes and characteristics of secondary electron emission and the formula for the yield due to primary electrons hitting on semiconductors and insulators, the universal formula for maximum yield [Formula: see text] due to primary electrons hitting on semiconductors and insulators was deduced, where [Formula: see text] is the maximum ratio of the number of secondary electrons produced by primary electrons to the number of primary electrons. On the basis of the formulae for primary range in different energy ranges of [Formula: see text], characteristics of secondary electron emission and the deduced universal formula for [Formula: see text], the formulae for [Formula: see text] in different energy ranges of [Formula: see text] were deduced, where [Formula: see text] is the primary incident energy at which secondary electron yields from semiconductors and insulators, [Formula: see text], are maximized to maximum secondary electron yields from semiconductors and insulators, [Formula: see text]; and [Formula: see text] is the maximum ratio of the number of total secondary electrons produced by primary electrons and backscattered electrons to the number of primary electrons. According to the deduced formulae for [Formula: see text], the relationship among [Formula: see text], [Formula: see text] and high-energy back-scattering coefficient [Formula: see text], the formulae for parameters of [Formula: see text] and the experimental data as well as the formulae for [Formula: see text] in different energy ranges of [Formula: see text] as a function of [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] were deduced, where [Formula: see text] and [Formula: see text] are the original electron affinity and the width of forbidden band, respectively. The scattering of [Formula: see text] was analyzed, and calculated [Formula: see text] values were compared with the values measured experimentally. It was concluded that the deduced formulae for [Formula: see text] were found to be universal for [Formula: see text].