Abstract: Comparing with the series expansion of the exact period,a new approximate fornmla and its modulated form for the period of the simple pendulum are presented.The constructed formula and its modulated form can be applied in the amplitudes of 114° and 136°,respectively,its relative error is less than 1‰.Some analyses on constructing of the period of a simple pendulum are discussed.

Key words: simple pendulum, period, approximate solution, series expansion