Abstract: A comprehensive analysis and discussion have been conducted on the approximate formula for the period of a large-angle pendulum in the literature. In terms of analytical form, the arithmetic-geometric mean recursive method is used. Although it has the highest accuracy, other simple approximate formulas can be selected when considering the convenience of calculation, simplicity of the formula, and the need for experimental measurement accuracy.

Key words: single pendulum, period, approximate formula, elliptic integral, arithmetic-geometric mean