We present an analytical model for calculating the entropy at melt of monatomic liquids. The model is motivated by the concept of a rough potential energy surface. It offers a simple, physical explanation for Richard's melting rule and provides a material-dependent correction to Trouton's vaporization rule. Without employing any adjustable parameters, the model agrees closely with experimental entropy of melting values for monatomic liquids. When combined with the phonon theory of liquids, it allows for estimation of entropy over the entire liquid range.