I am looking for the formula, not a rule of thumb. Is there a way to calculate the no-load current?
As both Andy aka and Bimpelrekkie have commented, there is no useful formula because there are far too many variables both known and unknown. It depends on the design and type (not all motors are induction) of the motor and how well it has been maintained. By far the easiest way of finding out is to get yourself a clamp on ammeter (readily available from multiple sources) and actually measure it on the particular motor in which you are interested.