calculator-user-registers is a variable defined in `calculator.el'.
Its value is

An association list of user-defined register bindings.
Each element in this list is a list of a character and a number that
will be stored in that character's register.

For example, use this to define the golden ratio number:
(setq calculator-user-registers '((?g . 1.61803398875)))
before you load calculator.

You can customize this variable.