What is the formula used to determine the maximum allowable amperage for a given circuit?

There is no single 'formula' for this, as the maximum current a circuit can handle depends on the temperature the various components within that circuit can operate at, without deterioration. There are so many factors involved, such as the type of component, the type of insulation, whether it can cool naturally or whether it must be force cooled, etc. Every circuit must be considered on an individual basis.