Zusammenfassung: This formula is based on the Richards formula, which includes well-known growth formulae, and is invariant for allometry. It is expanded by exchanging the independent variable from time to its function, in other words the cumulative water temperature. This standard formula includes the method of substituting values for the cumulative water temperature into the time term, the mathematical model of adding sine functions to the time term, and switched growth rate models. This standard model is given by general theory, which makes the character of parameters clear and helps to analyze the growth formula statistically.