Assuming you are using ArcMap since you mentioned field calculator:
Right click the field you wish to change to -1 and calculate that field.
Switch the radio button to Python
In the code block enter:
def changefield(whatif,okthen):
if (whatif == 0):
okthen = -1
return okthen
Then in the text box below FIELDB =
Enter: changefield(!FIELDA!, !FIELDB!)