Smiffy,

It's not that difficult. The frequency describes the rotational speed of the magnetic field provided by the controller to the motor... so top whack of 400Hz = 400 cycles/second, or 24000 cycles per minute.

However, motors are typically 2 pole or 4 pole - describing either a magnetic N/S pair (180 degrees apart) or a N/S/N/S 2-pair (90 degrees apart). When considering the actual RPM of the rotor, divide the rotational speed by the number of pole-pairs. So, 24000 cycles/min = 24000 RPM for a 2-pole motor, or 12000 RPM for a 4-pole motor.

That's why you'll find single-phase mains AC motors at 1500RPM or 3000RPM, depending on if they're 4-pole or 2-pole (respectively).

Some/many spindle controllers will allow you to program the number of pole-pairs - that's necessary to determine the RPM from the frequency.