I supposed you are referring to internal stairwell.
When there is a fire, the stairwell by regulation should be pressurised to the needed pressure to prevent smoke from entering. There are a few other considerations. When the fire alarm starts, the pressure in the stairwell should not be too great that the doors (usually 2 doors), which usually swing inward, be difficult to push open. There is a push force requirement. When the doors are opened, the air rushing out have a minimum required speed to blow away any smoke. Now the problem is, those doors nearer to the pressurising fan (usually located at the top) will be pressurised more. We are talking about air here, not water. So pressure is not equal throughout the stairwell. Duct will be needed for every landings to adjust the air flow. I do not know of a formula to calculate the fan size. In one of my project, I use a pressure sensor for the stairwell and a variable speed fan, many many times the size needed for the airflow. When the doors are closed, the fan run in a low rev pressure mode and pressurised the stairwell. When the doors are opened, the sensor senses the pressure drop and the fan runs in a higher rev and increase the air flow. When the doors closed again, the pressure increased and the sensor tells the fan to drop its rev so as not to violate the push force limit. It is good to use a more powerful fans because you do not know which doors will be opened. If the fan is oversize and since it is variable speed, then it will still work.