Erm, okay....a synchronous motor has no slip, hence the name. I dunno where other people are getting their info from, but the answer is simple:
@ 60Hz the formula is 7200 divided by the number of poles (where 7200 rpm would bve the theroetical speed of a single pole motor)
(hz x 120)
---------------- = synchronous speed num. poles
synchronous speed x percent slip
------------------------------------------ = full-load RPM 100
or when variables are known:
RPM (SYN) - RPM (FL)
-------------------------- x 100 = % slip RPM (SYN)
Does not get any simpler than that. This is easy math, you should not need to even ask this question....Dunno why this was so hard for anyone else to answer....
Percent slip is derived solely from the difference in synchronous speed vs full-load speed. Slip has little to do with voltage supplied to the motor, it is a factor of the twist in the rotor's squirrel-cage. Altering voltage from design voltages alters slip slightly, but base slip is determined by measuring rotor skew. Frequency has absolutely no effect on slip.
Class A motor? I think you might be mistaking your terminology. Class A refers to magnet-wire insulation class...
Design A motors are of a normal torque and slip of about 3% and have starting currents not limited by NEMA
Design B motors have a low starting current, normal slip, and normal torque. The typical general-purpose motor.
Design C has high starting-torque, low starting current, and low slip. This design is usually for sticky loads that are hard to start.
Slip does not change much until you get to design D, which are the high-torque, low starting current, high-slip motors where slip goes up to 13% or so.
Design letters are not a scale of slip, contrary to what seems popular belief. They are categories for various load requirements as set by NEMA