I have a servomotor connected to a gearbox and then a linear actuator.
how do I know the distance travelled of one shaft revolution?

 

That depends on the ratios of the gearbox and actuator. Do you have ratios or part numbers?

 

Not in hand, but what would be the equation?

 

The equation would depend on the physical configuration of the gearbox and linear actuator.
The distance traveled by the actuator for one revolution of the motor = gearbox ratio x distance traveled by actuator for one revolution of its input..

 

IOW, you need the pitch/thread of the screw !